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piis  fiasiiisiusi 


SOUND 

AND  ITS  RELATION  TO 
MUSIC 


v,\ 


CLARENCE  G.   HAMILTON,  A.M. 

ASSOCIAlJv    I'ROFluSSOK    t)F    MfSIC    AT 
WKIJ.liSI.KV   C()r,LH(iK 


BOSrON 

OLIVER   DITSON  COMPANY 


N]<;\V   YORK  CIIICAG) 

CHAS.   H.   DITSON    &   CO,  LYON    &   HEALY 

MADE  IN  U.   S.   A. 


'  Copyright.  MCMXII 
By  Omvkk  DiTSox  Company 

Inie))iatio!ial  Copyright  Secured 


DEDICATION 


To  my  very  dear  friend 
Professor  Hamilton  C.  MacDougall 


PREFACE 


Every  intelligent  musician  should  be  familiar  with  the 
physical  laws  which  underlie  his  art.  In  the  following  pages 
will  be  found  a  compact  statement  of  these  laws  and  of  the 
chief  facts,  theories  and  experiments  in  accordance  with  which 
thev  have  been  formulated.  The  nature  and  transmission  of 
sound,  its  various  elements  and  manifestations,  the  musical 
materials  derived  from  it  and  the  application  of  these  mate- 
rials in  the  construction  of  instruments  are  some  of  the  matters 
discussed. 

In  order  to  facilitate  further  reading  in  regard  to  any  of 
the  subjects  broached,  references  are  given  at  the  end  of  each 
chapter  to  correlative  parts  of  important  works  on  acoustics, 
of  which  a  list  is  appended.  Abstruse  mathematical  works 
like  those  of  Airy  or  Lord  Rayleigh  are  excluded.  Books  are 
referred  to  in  individual  chapters  simply  by  the  last  names  of 
their  authors 

Scientists  and  musicians  have  been  slow  in  cooperating,  and 
at  times  have  even  antagonized  each  other.  It  is  hoped  that 
in  the  future  mutual  helpfulness  will  take  the  place  of  distrust, 
and  that  due  allowance  may  be  made  by  either  party  for 
slight  points  of  divergence  between  mathematics  and  aesthetics. 
That  the  present  l)ook  mav  aid  toward  this  result  is  the  earnest 
wish  of  its  author. 

Clarence  G.   H.vmiltox. 

\\'elli;slev,  Mass.,  June,   1911. 


CONTENTS 


Pkefack     V 

List  of  Kffekexce  Books  vii 

J.     The  Ohigix  and  TRAxs>rissiox  of  Sotxd 1 

II.     A'elocitv,  Reflectiox.  Refka(ti(jx   AXi)  Diffhactiox 12 

III.  Pitch    24 

IV.  T.OL'DXESS.    I  XTEKFEI^EXCE   AXI)    RfSI'LTAXT   ToXES.  , 37 

y.     Qtalitv   51 

\'l.     Kesoxaxce   ')9 

\'\  1.     Scales.  Fxtek\als  axd  Chords    89 

A'lII.     The  1-".ak  axd  the  A'oice  108 

IX.     Mi'sicAL   Ixstkumexts  123 

I  xdex    147 


LIST  OF    REFERENCE    BOOKS 

Barnes,  C.  L.    Practical  ^Icoustics. 

Macmillan  and  Company.  London,  1909.     $1.10. 
Consists  mainly  of  a  series   of  exjjeriments. 
llAKTox,  Enwix  H.     .-/   Text-book  on  Soioid. 
Macmillan  and  Company.  London.   1909.     $3.00. 
A  highly  technical  treatise.      Illustrated. 
Llaskkxa,  P^iKTKo.     Tlic  Tlicovy  of  Sound. 
D.  Appleton  and  Company,  Xew  York,  187f).     $1.50. 
Readable  and  non-technical.     Illustrated. 
Mroadhol'se.  John.     Musical  Acoustics. 

William  Reeves,  London,     l-'ourth  editicjn,   1905.     $3.00. 
"The  Student's  Helmholtz."     Illustrated. 
Catchi'ool.  Ei)ML-.\I).     .1    Text-book  of  .Sound. 
W.  IC  Clive,  London,   1894.     $1.50. 

Somewhat   technical   in   character.      Illustrated. 
1-lAKKis.  T.  V.     Handbook  of  .Icousiic.'i. 

J.  Curwen  and   Sons.  London.     Revised   1910.     $1.25. 

A  well-outlined  treatment,  with   examination  questions.   Illustrated. 
Hkl.mholtz.  11.   L.  I".     Tlic  .Scusatio>is  of  Tone. 

Longmans,  Green  and  Company,  London.     Third  edition,  1895.     $9.50 
The  standard  work  on  acoustics, 
Lavigxac.  .Xi-iiKKT.     Music  and  Musicians. 

Henry  Idolt  and  Company,  London.     Revisetl   1907.     $1.75. 
The  hrst  part  contains  a  concise  treatment  of  acoustics. 
Pole.  \\'illia.m.     The  J'lulosol'hy  of  Music. 
Triibner  and  Company,  London,  1879.     $3.00. 
Discusses  the  materials  used  in  music. 

POYXTIXG    AXI)    TlIOMPSOX.       .Souud. 

Charles   Griffin   and    Comiiany,    London,    1909.     $2.75. 
Somewhat   technical,      I'ully   illustrated. 
Stoxk.  W.   II.     Elente.'tary  I.esso>is  on  Sound. 
^lacinillan   and   Company.   London.    1895.     $0.90. 
A   compact    treatise-.      Illustrated. 
Tavi.or.   Si:nLK\'.     Snuud  and  Music. 

Macmillan   and    Company.    London.    1883.     $2.50. 
Written   in  an  interestin.g  style. 
T'l  xnAi.L.  Jim  X.     .Soioid. 

D.   Aiipletdu   and   Comixmy.   New  Yf)rk.     $2.00. 
;\  standard  ])r>pular  work.     Illustrated. 
Zah.m,  J.  A,     Sound  and  Music. 

A.  C.   McClurg  and   Comiiany,  Chicago,   1892.     $2,00. 
\'erv  readable  and   fullv  illustrated. 


SOUND,  AND  ITS  RELATION 
TO  MUSIC 


CHAl'TER  I 

Th]-:  Okigix  AM)  Tka.xs.misskjx  of  Sound. 

TiikouGiiouT  the  recorded  course  of  human  histor}-,  in- 
vestigations into  tlie  nature  and  properties  of  sound  have 
occupied     the     attention     of     philosophers     and 

\  ,  ...  n         ■         Investigations 

scientists.     As  early  as  the  sixth  centurv  1j.  L..    of  sound- 

1  ^  111  r      '  1-  phenomena. 

lythagoras  demonstrated  the  laws  of  sounding 
strings ;  and  it  is  probable  that  his  researches  were  founded 
upon  data  derived  from  the  h^gyptians.  Others  of  the  (Ireek 
philoso])hers,  as  well  as  those  of  following  centurie.-.  pro- 
pounded and  s]5eculated  upon  the  various  and  complex  acoustic 
problems,  sometimes  giving  to  them  answers  which  have  after- 
ward been  found  logical  and  demonstrable.  It  wa>  onK  during 
the  intense  scientific  activity  of  the  latter  half  of  the  nineteenth 
century,  however,  that  a  reallv  competent  exposition  'of  the 
subject  appeared.  Tn  1862  the  distinguished  German  scientist 
Helmholtz  (1821-1894)  published  his  epoch-making  work  on 
The  Sensations  of  Tone.  This  was  supplemented  bv  the  labors 
of  other  enthusiasts,  such  as  Tyndall  (1820-180,3)  in  England 
and  Koenig  (  18.32-1901  )  at  Paris.  1'}-  interesting  and  convinc- 
ing experiments  these  men  succeeded  in  clearing  \\p  m_\-steri(nis 
points  which  had  bahfied  the  wits  of  sages  for  centuries,  and 
in  bringing  to  light  manv  facts  destined  to  aid  immea<urabl_\' 
the  comj)rehension  of  that  most  elu.-ive  of  all  the  art>.  music. 
Idle  fundamental  ])ro|)osition  upon  which  all  these  researches 
rest  is  that  the  physical  basis  of  sound  consists  in  a  form  of 
motion.   This  fact  is  so  patent  as  scarcelv  to  need    ^       .      t 

'  -  Sound    a    form 

further  dcmon>tration  :  we  can  easilv  observe  the    °^  motion, 
whirring  of  thiC  \iolin  string  a<  it  is  agitated  bv  the  Ikuv,  and 


SOCXD.  AM)  ITS  Rl-LATIOX  TO  Ml'SIC 


can  feel  the  trembling  of  the  bell  after  it  has  l)een  struck  by 
the  clapper;  nevertheless,  a  few  simjile  experiments  nia\-  still 
further  attest  its  truth. 

Let  a  pith  ball  be  suspended  so  that  it  hangs  close  to  one  of 
the  ])r()ngs  of  a  tuning-fork.  (big.  1.)  Jf  now  a  A-inlin  Ixiw 
c     f     c  ^u-        I't;  drawn  across  the   fork  so  as 

Proofs   of  ttiis 

from  sounding       ^,,  i)roducc  a  toue.   tlic  ball  will 

tuning-fork  and  ' 

^'"■'"s-  be  thrown  \iolently  to  one  side. 

and  will  be  repeatedly  re])elle(l  whenever  it 
rebounds  against  the  fork,  thus  showing  that 
the  fork  is  in  a  state  of  agitation  while  sound- 
ing. ( )r.  let  a  chalked  string  be  suspended 
over  two  bridges  ./  and  B  (Fig.  2)  in  front  of 
a  blackboard,  with  one  end  of  the  string  wound 
about  a  pin  at  C.  which  can  thus  regulate  its 
tension.  If  the  string  be  now  plucked  in  the 
middle,  its  vibrations  will  be  seen  ])lain1y.  and  ^'"-  '■ 

when  the  tension  is  increa>ed  by  ttirning  the  pin  ( '.  the^e 
vibrations  will  become  still  more  rapid. 

liesides  taking  its  rise  in  the  motions  of  solid  l)odies.  sound 

ma\-  also  be  prc^duced  b_\-  the  shock  t)ccasioned  when  a  liberated 

gas  comes  violentlv  into  contact  with 

Sound   from  ...  ,     '  . 

Kases  or  from       the  au'  ui  au  ex])losion,  or  even  bv  the 

confined    air.  ...  ,  .  '  . 

agitation  of  a  se(|uestrated  ])ortion  ot 
the  air  itself,  such  as  occurs  in  an  organ  pipe.  -\n 
illustration  of  this  latter  phenomenon  will  be  found 
on  i)age  7S. 

bet  us  now  return  to  our  tuning-fork.  Aflixing 
a  little  metal  point  to  each  prong  and  drawing  thc>e 
^       .    ,.         ,    points  rapidlv  over  a  i)iece  of  smoked 

bxammation    of      ^  ■  -  ' 

glass  while  the  fork  is  sounding.  \\e 
produce  a  wa\v  line,  as  in  Fig.  -v 
F.xaniining  this  line,  we  fmd  that  it  is  composed  o{ 
regular  curves  which  run  alternatel}-  to  one  side  and 
to  the  other.  Our  deduction  from  this  di-co\ery  i>  ^fews 
that  each  prong  swings  continuall_\-  to  and  fro,  in  the 


the    vibrations 
of    a    tuning- 
fork. 


SOr.M).  .IM)  ITS  RliL.irioX  TO  Mr  SIC  3 

manner  of  a  ])enduluni.      Starting   from  a   jHjint  of   rest,  it  is 


imj)ellefl  b_\'  the  ^■iolin  bow  a  given  distance  in  one  direction, 
where  it  becomes  motionless  for  an  instant.  It  then  rebounds 
to  its  hrst  position,  and  immecHatcl}-  performs  a  simiUir  e\'olu- 
tion  in  the  o])])osite  chrection.  When  it  has  again  returned  to 
its  starting  jjoint  it  lias  made  what  is  called  a  complete  vibra- 
tion. If  it  should  then  stop,  the  air  ^\■ould  carry  a  single  ex- 
])losive  blow  to  our  ears  ;  but,  impelled  1)\-  the  impetus  which  it 
has  receix'ed,  the  i)rong  continues  to  vibrate  with    .,    .   ,. 

'■  '^  Periodic 

les>ening  force,  until  it  returns  t(j  rest,  or  until    ^''bration. 
the  bow  again  agitates  it.     A  number  of  vibrations  of  similar 
character   thus  occurring  in   regular   secjuence   are   said   to  be 
periodic,    and   the    sound    which    thev   produce    is   of   uniform 
pitch. 

Let  us  note  that,  in  order  to  be  capable  of  i)erforming  such 
vil)rations.  a  bodv  must  pcx-^sess  what  is  called  elasticity,  which 
means   the   power   of   rebounding  to   its   original 

.  ^  Nature    of    the 

position   after   some    torcc   has   driven   it   to   one    property  of 

.  .  -       1   •  ■  •  ■  elasticity. 

Side.      An  instance  ot    this   action   is  seen   m   an 
ordinar\-,  ela>tic  banrl.     W'c  make  u-c  of  this  to  hold  objects 
together  b\-  the  force  which  it  C(^nstantl\-  exerts  after  it  ha? 
been  stretched,  and  which,  if  allowed  to  do  so,  would  snap  it 
hack  vigorouslv  into  its  normal  condition. 


4  SOiWn.  AXD  ITS  RIILATIOX  TO  MUSIC 

The  vibrations  of  the  tuning-fork  which  we  examined  were 
all  simple:  that  is.  they  produced  i)erfectl}-  uniform  cur\es  on 
Tone  and  either  side  of  the  wavy  line.     As  a  matter  of  fnct, 

"°'^^-  however,  such  simplicit}-  is  seldom  founrl  in  the 

motions  of  a  sounding  Ijod}' ;  for,  as  a  general  rule,  these 
are  accompanied  h}-  other  vibrations  of  diiterent  extent  and 
rapidity,  while  sometimes  a  mingling  of  all  sorts  of  motions 
takes  place.  The  sound  made  !)}•  the  impact  of  the  lingers 
upon  the  piano  keys,  for  instance,  is  mingled  with  the  musi- 
cal tones,  as  is  the  scraping  of  the  violin  bow  acr()s>  the 
strings,  and  the  hissing  of  the  air  at  the  mouth  of  the  organ 
pipe.  When  the  vibrations  are  ])eriodic,  and  are  cither  ^-im])le 
or  else  accompanied  b}"  suljordinate  vibrations  which  are  in- 
distinguishable or  have  simple  relations  to  the  primal  sf)und. 
the  complete  sound  is  said  to  be  iiiiisica!  in  character,  and  its 
fundamental  ettect  is  si)oken  of  as  a  tmic.  According  as  the 
more  complex  or  irregular  \-ibrations  become  promment  in  the 
sotmd.  does  it  lose  in  its  musical  value  :  and  when  all  semblance 
(jf  regularity  has  disapi)eared.  tone  \'ani-lic-.  and  the  ><iund  is 
described  as  mere  noise.  It  is  exident.  therefore,  that  no  sharp 
line  of  demarkation  exists  Ijetwecn  musical  and  non-mu-ical 
sounds,  and  that  a  classification  (jf  the  doubtful  ca:-es  mu>t 
depend  largelv  tipon  personal  o])inion. 

When  we  incjuire,  on  the  other  hand,  what  kinds  of  ^Dunds 
are  available  for  the  use  of  the  mu-ician.  otiicr  con.-ideration- 
c       ,  .,        arise.     Mowever  musical  the  tone,  it  must  be  i)Ut 

Sounds     avail-  ' 

able  in  music.  jjif,,  .^  jiracticablc  fomi.  The  .-ound  gi\cn  out  b}- 
the  falls  of  Niagara,  for  instance,  has  lieen  analyzed  and 
found  to  have  decided  musical  characteristics,  -ince  ii  jjo^- 
sesses  a  stronglv-marked  fundamental  tone  and  liarnn  iniou- 
accompanx'ing  tones;  but  thi^  rich  combination  could  hardl}' 
be  intrcxluced  into  a  musical  com])osition.  cxccjit  b\  jirow. 
The  sub-^titutes  for  an\-  desired  sounds  of  nature  nui-^t  be  fi  aind 
in  either  the  human  voice  or  artiticial  nni-ical  instruments. 
These  latter  have  been  de\-i-ed  and  elaborated  to  such  an  extent 
that   the  mridern   comjio-er   has   at    hi-   command   mo^t   .it    the 


socxn.  ./AV  ITS  h'/iL.iriox  to  MCSIC  5 

typical   varieties   of   tone,   each   tlirous^h    an   adecjtuite   compass 
of  pitches. 

In  his  coni])o>itions.  therefore,  the  musician  makes  use  in  the 
first  i)lace  of  instruments  hke  the  \-iohn,  which  can  i)ro(luce 
tone  i)ure  in  its  make-U])  and  steadv  in  its  ])itcli. 

\'  1  1  1  •  '  1  -  Types    of 

.Next,    ho\ve\er,    lie    emplo\"s    >pecial    means    tor    musical 

,         .     .  ".       ,  .  .  instruments. 

cm])hasizmi;'  the  element  ot  rlivtiiiii ;  tor  it  niu>t 
be  remembered  that  rcyuhir  pulsation  is  as  important  a  factor 
in  musical  structure  as  melodic  beaut}'.  Thus  in>truments  of 
l)crcus>ion  are  also  necessar}-,  in  which  an  ex])losive  sound 
mark.-  off  the  dix'isions  of  time.  Some  of  these  instruments, 
like  the  kettle  drum,  have  a  distinct  fundamental  tone;  while 
others,  like  the  snare  drum,  give  out  merely  a  confused  noise. 
Then,  too,  while  the  coni])()ser  Ijases  his  work  u])on  conven- 
tional instruments,  he  feels  at  libertv  to  introduce  those  of  a 
bizarre  character,  like  the  tam-tam,  or  queer  elTects,  like  the 
rapping  of  the  \'iolin  bow  on  the  wood  of  the  violin,  in  order 
to  express  some  extraordinarv  conception.  The  sounds  which 
he  is  least  likeK-  to  em])loy  are  those  which  are  unreliable  in 
pitch,  like  tho.-e  of  the  siren  (page  26),  since  such  sounds  are 
subversi\-e  of  those  dehnite  intervals  which  form  the  sub- 
structure of  music,  and  give  to  it  stability 


For  the  present,  we  shall  consider  only  those  sounds  which 
are  produced  Iw  simple  vibrations.     We  pass,  therefore,  to  the 
discttssion  of  the  manner  bv 

Necessity    for 

which  these   \'ibrations  are    a  medium  as  a 

sound-trans- 
able  to  reach  our  ears,  when    mitter.    Proof 

.     .  .  .  .  of   this. 

originating  m  objects  en- 
tirelv  external  to  oursch'es.  (lenerally, 
the  sound  reaches  us  through  the  inter- 
vening air,  and  it  can  easily  be  shown 
that,  while  other  media  mav  serve  as 
sound-transmitters,  a  medium  of  some 
description  must  be  employed  for  the 
purpose,  and  that  without  this,  no  sound  can  be  heard.     In 


SOUXD,  .LXD  ITS  RELATIOX  TO  MUSIC 


Fig.  4  a  bell  7",  placed  ui)on  a  plate  that  is  connected  with  an 
air-pump,  is  kept  sounding  by  means  of  a  clock-work  attach- 
ment //  C';  and  over  the  whole  a  bell-glass  is  placed.  The 
sound  at  first  continues  with  almost  undiminished  intensity, 
but  as  the  air  is  exhausted  by  the  pumi),  the  sound  grows 
fainter,  and  when  a  practical  vacuum  is  produced,  it  is  in- 
audible. Care  has  been  taken  to  place  the  clock-work  upon  a 
piece  of  non-conducting  material,  otherwise  the  vibrations 
would  have  been  carried  to  the  outer  air  by  the  plate  itself. 
If,  now,  h}"dr()gen.  which  is  fifteen  times  lighter  than  air,  be 
admitted  within  the  glass,  a  faint  sound  is  heard.  Hence  we 
c(jnclude  that  the  sound  decreases  as  the  medium  through 
which  it  passes  becomes  attenuated.  This  latter  fact  has 
been  further  attested  by  experiments  with  other  gases  and 
vapors.  Solids.  al<o,  are  often  good  transmitters  of  sound. 
Deaf  ])ersons,  for  in>tance,  are  enabled  to  hear  distinctl}'.  when 
the  auditor\-  nerve  is  unimpaired,  bv  holding  an  apparatus  be- 
tween their  teeth  which  catches  the  sound-vibrations  from  the 
external  air,  whence  thc\-  are  conx'eyed  to  the  ear  through  the 
intervening  bones  of  the  head. 

To  understand  how  vibrations  are  imparted  to  the  air  b}-  £ 

^ounfling  l.)od}',  we  must  lirst   remember  that  the  air  is  com 

posed     of     an     inconceivablv  ».....4^....,,^ 

Action    of   a  ,  ^  .    ,  ' 

vibrating  rod        great  uumbcr  of   particles  or 

upon    the    air.  '  . 

molecules,  r(jughh-  estimated 
as  a  million  Ijillions  to  a  cubic  centimeter,  or 
cube  one  side  of  which  i<  about  three-eighths 
of  an  inch  long.  Placing  a  metallic  bar 
.  /  -B  in  a  vi>e  E  C  (  Fig.  5  ).  we  set  the  free 
])art  ./  ("  into  a  ])endulum-like  motion  by 
drawing  it  to  one  side  at  the  ]:)oint  .-l .  If 
the  free  ])art  has  ijecn  made  long  enough. 
we  can  easily  see  this  oscillate  from  a  to  a'. 
and  no  -ound  will  be  heard.  The  reason 
for  this  latter  fact  is  that  the  vibrations  are 
made   so   slr)\vl\-   that   the   air-particles   have 


SOUND,  AND  ITS  RliL.lTfOX  TO  MUSIC 


time  to  slip  out  of  the  way  before  the  onset  of  the  bar.  If  now 
tlie  free  part  be  made  gradually  shorter,  the  vibrations  will 
grow  faster,  and  will  linally  be  so  blended  together  that  they 
are  indistinguishable.  At  a  certain  point,  too,  a  low  t(jne  will 
be  heard.  This  tone  arises  ivoni  the  fact  that  the  air-particles 
no  longer  have  time  to  avoid  the  bar  as  it  approaches,  and  are 
therefore  hit  by  it  at  each  of  its  attacks.  When  the  particles 
next  to  the  bar  are  thus  affected,  they  are  thrown  violently 
against  those  next  to  them,  which  in  their  turn  transmit  the 
impulse  to  their  neighbors.  This  crowding  together  of  par- 
ticles, or  condensation,  as  it  is  called,  now  passes   „,  , 

'  '  i  The    wave    of 

along    rapidly    from    one    series    of    particles    to    condensation, 
another  in  all  directions  away  from  the  bar. 

Hut  after  the  rod  has  forced  together  the  particles  which 
obstruct  its  passage,  it  immediately  springs  back  in  the  oppo- 
site direction,  leavins^  in  its  track  a  s])ace  which    _,,  , 

o  '  1  he   wave   oi 

is  rendered  practicallv  emptv  of  particles,  and  rarefaction. 
which  is  thus  said  to  be  rcrcficd.  This  wave  of  rarefaction 
follows  immediately  after  that  of  condensation,  just  described. 
.Again  the  rod  attacks,  and  an(jther  wave  of  condensation  starts 
out,  succeeded  as  before  Ijv  a  wave  of  rarefaction  ;  and  these 
alternate  conditions  are  repeated,  so  long  as  the  rod  continues 
to  A'iljrate. 

The  manner  in  which  the  waves  proceed  from  the  sounding 
object  to  the  ear  of  the  listener  is  graphicalK-   portrayed   in 

Fig.  6.  One  of  the 
prongs  of  the  tun- 
ing-fork here  rep- 
resented produces 
vibrations  in  ex- 
actly the  same  wav 
as  the  metal  bar 
which  we  h  a  v  e 
taken  as  our  model. 
In  actual  computa- 
Fig.  6.  tions,     a    comi)letc 


r\ 


SOUND.  .1X1)  ITS  RliLATlOX  TO   MUSIC 


sound-wave  is  made  to  consist  of  the  sum  of  a  condensation 
and  a  rarefaction.  I  lence  the  length  of  a  sound-wave  will 
be  equal  to  the  distance  from  any  given  point 

...  ...  Action    and 

m   a    condensation    to    a    similar   point    in   the    length  of  a 

.  p  .  .  .  sound-wave. 

next  condensation,  or  irom  a  given  point  m  a 
rarefaction  to  a  similar  point  in  the  next  rarefaction. 

It  is   important  to  notice   that  the   air-particles,   when  thus 

acted    ui)on,    do    not    move    permanentK-    rrom    their    original 

.,      .  i.)ositions.      If    they    were   blown   alonij   1)\-   each 

The    vibration  '  -  J5        . 

of  air-particles,  souud-wave,  wc  sliould  fcci  a  draught  of  air 
with  each  "sound  which  reaches  us.  I  kit  tlie  particles  act 
much  as  do  the  blades  of  wheat  when  a  breeze  sweeps  over 
the  wheat-tield.  driv- 
ing these  aside  only 
temporarily.  in  the 
case  of  the  air-parti- 
cles, however,  each 
performs  a  complete 
vibration  for  each 
sound  -  wave,  corre- 
sponding to  that  of 
the  sounding  bod}-. 
1  low  this  motion  is 
accomplished  can  l)e  seen  by  the  use  of  I  lie  stand  shown  in 
I'lg.  7,  invented  l)y  Alariotte  over  two  hundred  years  ago. 
In  this,  an  im])ulse  given  to  one  of  the  balls  A  travels  through 
the  entire  line  of  balls,  while  each  one  is  stoi)pcd  in  its  course 
by  the  push  which  it  transmits  to  the  next.  Only  the  end  ball  C 
llics  olt  to  a  greater  distance,  the  others  l)ccoming  motionless. 
Thus  does  the  sound  reach  the  ear.  while  the  intervening  air 
])articles  return  to  th.eir  original  ])laccs  unless  again  set  in 
vibration  bv  the  sounding  body.  Sound-waves  arc  also  frc- 
(juentlv   compared    with   the    waves   which    arise 

Sound-waves  '  .       ,  ,    .  ,  \  •   i 

comnared   with     whcu  a  stouc  IS  drop])ed  luto  the  water.     As  with 

water-waves.  .  .    ,  ,  .    ,  -  •, 

air-particles,  the  water-particles  i)erh)rm  an  oscil- 


n-        -   - 



1 

! 

)i 

A 

)(■ 

x- 

)C 

! 
i 

[ 

/- 

1 

y 

Fig.   7. 


latin"' 


lution,  returning  Pnallv  to  their  normal  places.     lUit 


SOCXD.  ,1X1)  ITS  RliLATIOX  TO  MUSIC  9 


F--.    8. 


10  SOUND,  AND  ITS  RELATION  TO  MUSIC 

while  the  water-particles  have  an  up  and  down  motion,  the 
air-particles  move  forward  and  hack ;  and  also,  while  the 
water-waves  move  simply  along  the  surface  of  the  water,  the 
sound-waves  swell  out  into  the  form  of  a  sphere,  of  which 
the  radius  is  constantly  and  rapidly  increasing. 

Under  ordinary  circumstances  sound-waves  are  impercep- 
tible to  any  of  the  senses  except  that  of  hearing.  Heavy 
,,.  ...  detonations,  however,  such  as  the  roll  of  thunder 

Visible  '  ' 

Sound-waves.  ^j-  ^j^g  rcport  of  a  cannou,  can  be  felt  as  well  as 
seen ;  and  in  certain  cases  sound-waves  have  become  visible. 
Professor  C.  \'.  Boys,  in  1897,  succeeded  in  obtaining  a  series 
of  kinematograph  pictures  of  the  explosion  of  a  hundred  and 
twenty  pounds  of  a  nitro-compound,  taken  at  the  unusually 
rapid  rate  of  eighty  exposures  j^er  second.  In  .-/^  of  the  first 
ten  of  these,  shown  in  Fig.  8,  .1  to  J,  the  smoke  of  the  explosion 
appears  rising  gradually  on  the  right.  In  the  series  B  to  J  the 
sound-wave,  in  the  form  of  a  light  ring,  is  seen  rapidly  ex- 
panding beyond  the  smoke  of  the  explosion.  Professor  Boys 
says,  "We  stationed  ourselves  as  near  as  prudence  would  allow, 
at  a  distance  of  one  hundred  and  tw^enty  yards,  so  that  only 
about  one-third  of  a  second  elapsed  between  the  detonation 
and  the  passage  of  the  shadow.  The  actual  appearance  of 
the  ring  was  that  of  a  strong,  black,  circular  line,  opening  out 
with  terrific  speed  from  the  point  of  explosion  as  a  center."* 
In  the  pictures  the  black  line  does  not  appear,  but  only  the  light 
ring  which  must  have  accompanied  it. 


*See  articles  by   Professor   Boys   in  Nature   for  June  24.   lcS97,   and 
by  Prof.  R.  W.  Wood,  in  Popular  Science  Monthly  for  August,  1900. 


SOUND,  AND  ITS  RELATION  TO  MUSIC  11 

SUMMARY 

Sound  is  always  produced  1)\  the  vibratory  motion  of 
particles  of  matter,  either  in  a  mass  or  as  individuals. 

Musical  sound,  or  tone,  is  produced  by  regular  and  periodic 
vibrations,  and  non-musical  sound  by  irregular  vibrations ;  but 
the  lines  of  demarkation  between  the  two  are  not  sharply 
drawn,  and  the  musician  may  employ  for  special  effects  many 
kinds  of  sound  usually  classified  as  noise. 

Some  medium  is  necessary  for  the  transmission  of  the  sound 
from  its  origin  to  the  ear  of  the  auditor.  This  medium  is 
generally  the  air,  in  which  the  sound  travels  in  waves,  each 
consisting  of  the  sum  of  a  condensation  and  a  rarefaction. 

In  this  transmission,  the  air-particles  also  move  in  vibra- 
tions. The  sound-waves  form  a  constantly  enlarging  sphere; 
and  their  motion  is  generally  perceptible  only  to  the  sense  of 
hearing. 

REFERENCE  LIST. 

Helmholtz,  Chapters  1  and  2. 

Zahm,  Chapter  1. 

Tyndall,  Chapters  1  and  2. 

Taylor,  Chapter  1. 

Broadhouse,  Chapters  1-4. 

Harris,  Chapters  1  and  2. 

Catchpool,  Chapters  1  and  2. 

Stone,  Introduction,  and  Chapters  1  and  2. 

Poynting  and   Thompson,  Chapter  1. 

Blaserna.  Chapters  1   and  2. 

Barnes,  Chapters  1  and  2. 

Barton,  Chapter  1. 

Lavignac,  Chapter  1,  A. 


CHAPTER  II 

\"elocitv,    Rkflection,    Rkiractiox    and   Diffraction'. 

Till-  rapidil}-  with  which  sound  is  transniilied  through  any 
medium  is  dependent  upon  two  factor.-,  the  one  of  which  is 
„  tlie    dciisitx    of    the    medium,    and   the    other    its 

Factors 

affectms  clasticitx.     (Jf  the.-c,  the  former  tends  to  retard, 

velocity     01 

^°""'^-  and  the  other  t<.)  accelerate  the  sound. 

W  c  have  stated  that  aU  matter  i>  made  up  of  a  vast  cjuantitv 
><i  inconceix'aljh-'  >mall  particles,  ihe  numher  (ji  tlvjse  present 
„     ,.  .        ,         in  a  gix'cn  hulk  of  matter  is  said  to  con-titiUc  its 

eondition    ot  '^ 

^■^"^■'y-  dnistty;  and  this  density  hucomes  greater  or  kss 

according  as  the  number  of  ])article>  increase.-  or  dimini-hes. 
A  change  of  condition  or  locaticm.  howe\"er.  ma\-  attect  this 
numher  to  ,-i  considerable  degree.  We  know.  ii<r  instance,  that 
the  air  on  a  uKiuntain  top  i<  mucli  lc>s  cler.-e  (  or  more  rarehed  ) 
than  that  in  the  \alle_\-  beneath. 

d'hriju^h  this  ma->  of  particles  the  sound-wa\es  proceed  at 
a  rate  which,  though  c.xtremcly  ra])id,  is  \et  ea.-il\'  aiJprecialde 
,.  ^     .  b\-  the  .-cn-e>.     We  have  all.  when  -eaterl  in  the 

Light     faster 

than  sound.  ^^.^y  ,,f  -^  large  concert  hall,  noterl  how  the  beat^ 

of  the  orchestral  condtict' ir  seemed  curiour-l_\"  to  precede  the 
sound.-  which  lhe\-  e\'okcd..  This  illusion  ari.-cs  froiu  the  same 
princi])le  wdiich  causes  ihc  lightning;'  tia-li  to  be  \"i-iblc  some- 
times many  .-cco'Uils  before  its  accompanying  cra-h  of  thunder 
is  audible:  namel\-,  that  li^ht  trax-e^-  r.iu  di  .'a-!i_-r  tlijin  -ound. 
The  \-elocitv  of  liglit.  c^imoule'l  ;:t  ;.i..iUL  l'-  M'J'il  niiles  per 
<econfl.  is  sm  great.  th;ii.  for  terre-iria!  di-iance.s.  the  lime 
^  which  it  <)ccui)ies  in  iraw'ling  f  r(  an  it-  -ource  to 

IJetermmation  ' 

of  sound-  ^j.,^  f^y,^  ^,j-  ^]^^  beliolder  i-  I'racticallv  ne^'ligible. 

velocity    by  -  .  .  .-> 

flash  of  light.  71-,]^  f-i^;!-  ,^.,,jy  iherefoi-e  be  u-e'l  \<  <  aflxTintage  in 
determining  -()iuKl-\'elncit\".  Let  a  cannon  be  tired  at  a  known 
distance,  and  the  time  which  elapses  lietwcen  the  tiash  anri  the 
report  be  recMrded.     Evidently,  if  the  entire  distance  be  divided 


SOUND,  AND  ITS  RliLATlON  TO  MUSIC  13 

by  the  ascertained  number  of  seconds,  the  result  will  be  the 
distance  traversed  in  a  single  second,  which  distance  is  gen- 
erally used  as  the  unit  of  measurement. 

l'\)r  purposes  of  extreme  accuracy,  however,  this  exjjeriment 
nuist  be  conducted  with  much  more  care.  Several  disturbing 
factors,  the  chief  ones  of  which  are  the  wind,  the    ,, 

'  '  txperiments 

tem])erature,  and  the  moisture,  are  almcjst  inva-  °'^  ''^'^  •'^^'^• 
riablv  to  be  reckoned  on.  The  most  important  of  these  is  the 
wind,  which  carries  the  sound  faster  when  it  is  moving  in  the 
same  direction,  and  retards  it  when  the  directions  are  in 
opposition.  In  the  first  accurate  experiments  tipon  the  velocity 
of  sound,  made  by  the  French  Academy  of  Sciences  in  1738, 
cannon  were  fired  at  three  stations  visible  from  the  Paris 
Observatory,  but  at  some  distance  away,  a  report  taking  place 
at  one  of  the  stations  every  ten  minutes.  The  time-intervals 
between  the  flashes  and  reports  were  recorded  and  afterwards 
a^'eraged.  In  a  similar  experiment,  in  1822,  it  was  sought  still 
ftu'ther  to  eliminate  the  inflttence  of  the  wind  by  firing  cannon 
alternately  at  each  of  two  stations  about  twelve  miles  apart. 
The  time  for  the  light  and  sound  of  each  report  to  reach  the 
opposite  station  was  noted,  and  the  mean  between  the  figure 
arrived  at  by  each  set  of  observers  was  finally  adopted.  In 
subsequent  experiments  even  more  pains  were  taken  to  secure 
exactness,  such  as  the  employment  of  electrical  devices  to 
record  the  arrival  of  the  flashes  and  reports,  in  order  to  elim- 
inate the  slight  error  arising  from  the  portion  of  time  necessary 
for  the  observer  to  realize  and  then  record  the  sensation 
received. 

The  velocity  of  sound  thus  determined  was  found  to  be 
1090  feet  per  second  when  the  temperature  of  the  air  was  at 
the  freezing  point.     This  velocitv  increased,  how-    „     , 

*   '  -  Resultant 

ever,  with   a   rising  temperature,   at   the   rate  of    figures, 
about   a   foot   for  each   degree   Fahrenheit.      Consequentlv,  at 
the  ordinary  temperature,  1120  feet  per  second  may  be  re- 
garded  as    sufficiently   accurate    for   rough    calculations ;   a 

speed  nearly  thirteen  times  as  fast  as  the  fastest  express  train. 


14  SOUXD.  .-/.\7)  /7.S-  RRLATIOX  TO  MUSIC 

If  the  number  of  seconds  between  the  perception  of  a  Hght 
and  its  sound  be  nuiltipHed  by  this  velocity  per  second,  the 
Determination  ^esult  will  evidently  be  the  distance  of  the  sound- 
of  a^loundtnr  '^^^  object.  W'c  may  thus  estimate  the  distance 
^°'^y-  of  a  lightning  discharge  by  counting  the  number 

of  seconds  between  the  flash  and  its  accom])an}ing  peal  of 
thunder,  and  allowing  something  less  than  five  seconds  to  a 
mile. 

Uefore  the  above  exi:)eriments  had  taken  place.   Sir   Isaac 

Newton   (1642-1727)  had  calculated  sound-velocity  bv  labora- 

torv  methods   and   had   secured   hgures   about   a 

Verification  •1111 

by  different  sixth  smaller  than  those  we  have  given.     It  was 

experiments.  .  . 

atterward  discovered,  however,  that  the  sound- 
wa\-es  themselves  produced  a  slight  rise  in  temperature  which 
effected  this  dift'erence.  Other  experiments  at  short  distances 
and  of  a  more  complicated  character  have  served  to  verify- 
the  accepted  figures. 

Father  ^lersenne  (1588-1648)  calculated  sound-velocity  b_\' 
noting  the  time  which  it  took  for  an  echo   (page  19)  to  reach 

him.   and   the   distance   of   the   reflecting   object. 

Velocity 

calculated  from     As  the  souud  must  travel  to  this  object  and  back 

echoes.  .  .        .    ,,  ...  "    .  .  , 

again,  it  tollows  that  a  division  ot  twice  the 
distance  of  the  object  bv  the  number  of  seconds  recjuired  for 
the  echo  to  return  will  give  the  velocit}'  per  second.  It  is 
hardl\-  possible,  however,  to  sectire  extreme  acctiracy  by  this 
method. 

While  a  variation  in  temperature  i)r<)duces  a  corresi)onding 

variation    in    sound-velocity,    it   is   nevertheless    trtie   that   the 

velocity  remains  the  same,  however  much  the 

Effect    of  ,  .  .      ,  .  ^  ^,., 

varying  den-  density  of  the  air  may  nuctuate.  1  he  cause  ot 
this  phenomenon  is  that  with  an  increase  in  the 
densit}-.  there  is  an  exactly  proportional  increase  in  the  elas- 
ticity of  the  air;  hence  the  ratio  between  the  two  factor'^ 
remains  constant. 

As  a  general  rule,  too,  whatever  the  pitch  or  other  char- 
acteristics of  the   sound,   its  velocity  is  the  same.      If  this 


SOUA'D.  AXD  ITS  RliLATIOX  TO  MUSIC 


I J 


were  not  true,  we  should  hear  sounds  at  a  (lis-    ,,,.,• 

'  Velocity   in   air 

tance  in   varvins:  order   from  that  of  their  pro-    "°*  affected  by 

'-'  i  character    of 

duction,  and  the  music  from  a  brass  band,  for  sound, 
instance,  would  reach  us  in  inextricable  confusion.  it  has 
been  pretty  well  proved,  however,  that  extraordinarily  l(jud 
sounds  may  have  an  increase  of  velocity  over  those  of  ordinary 
intensity.  An  interesting  example  of  this  exception  was 
afTorded  on  one  of  Parry's  arctic  voyages,  in  1822,  when,  at 
a  distance  of  two  and  a  half  miles,  the  order  to  hre  a  cannon 
was  heard  after  the  report. 

In  other  media  the  velocity  of  sound  is  frequently  much 
dififerent  from  what  it  is  in  air.  Experiments  made  b\-  means 
of   long   ttiljes    and   organ    pii^es    have    ])roduced   ,,  ,    .^    . 

"  oil  t  Velocity  in 

the  following  rates  per  second  in  gases,  at  the    sases. 
freezing  point  of  air,  or  0°   Centigrade  : — 

Oxygen   1040  feet 

Hydrogen    4164  feet 

Carbon  dioxide 858  feet 

Carbon  monoxide 1 107  feet 

Xitrous  oxide 859  feet 

Olertant  gas 1030  feet 

Important  experiments  as  to  velocity  in  water  were  made  by 
two  French  physicists  in  1827,  on  the  Lake  of  Geneva.  Sta- 
tioned in  boats  on  opposite  sides  of  the  lake,  one  velocity  in 
of  them  took  charge  of  the  sound-production.  I'^^'ds. 
while  the  other  recorded  the  results  with  a  stop-watch,  listen- 
ing through  an  ear 
trumpet  0  M  (Fig 
'-• ) .  held  in  the  water. 
The  source  of  sound 
was  the  bell  C  struck 
vj  by  the  hammer  B. 
J  The  lever  which  im- 
-I  pelled  B  simultane- 
2i  ously  ignited  a  flash 
Fig.  9.  of  gunpowder  by  the 


Gr 


16  SOUND.  AND  ITS  RELATION  TO  MUSIC 

torch  -1/.  It  was  thus  found  that  the  velocity  of  sound  in  water 
at  8.1°  C.  was  4,707  feet  per  second,  or  more  than  four  times 
what  it  is  in  air.  Different  figures  have  resulted  from  experi- 
ments with  other  liquids,  though  the  increase  of  velocitv  over 
that  in  air  is  considerable  in  each  case.  The  reason  for  this 
fact  is  that,  although  liquids  are  more  dense  than  air,  their 
elasticity  is  still  greater  in  proportion. 

In  most  of  the  solids,  the  same  conditions  exist.  In  metals, 
the  velocit}-  varies  from  four  to  sixteen  times  its  rate  in  air. 
,,  ,    ..     .  In  wood,  the  velocitv  is  greater  in  the  direction 

Velocity    m  '  .  ti 

^°''^^'  of  the  fibre  than  across  the  rings.    In  the  former 

direction,  it  varies  in  different  woods  from  ten  to  sixteen 
times  its  rate  in  air.  The  greatest  velocity  is  found  in  iron 
and  steel,  of  the  metals,  and  fir  and  as])en,  of  the  woods.  It 
should  be  noted  that  an  augmentation  of  temperature,  which 
increases  the  velocity  in  gases  and  liquids,  has  generally  the 
opposite  efifect  upon  the  velocity  in  metals. 

Wood  is  an  especiallv  good  conductor  of  sound.  To  illus- 
trate this  characteristic,  wrap  up  a  music  box  in  several 
-,  thicknesses  of  felt,  a  non-conductor  of  sound,  so 

Experiments 

with  wood.  ^]^^^   ^]^Q   sound   is   made   as   nearly   inaudible   as 

possible.  If,  now,  the  end  of  a  rod  of  wood  three  or  four 
feet  long  be  inserted  in  the  wrappings  and  rested  on  the  lid 
of  the  box  while  it  is  playing,  the  sound-vibrations  will  be 
plainlv  felt  along  the  rod  by  the  hand,  and,  on  a})plying  the 
ear  to  the  other  end  of  it.  the  music  will  be  heard  with  greatly 
increased  intensity.  Place  a  guitar  or  violin  against  the  free 
end  of  the  rod,  and  the  vibrations  will  be  tran.-mitted  to  it, 
so  that  the  music  seems  to  proceed  from  this  instrument. 

.\nother  instance  of  the  passage  of  sound  through  solids  is 

afi'orded   b\-  the   familiar  string   tcleplioitc.   which   consists   of 

two  cardboard  tubes,  each  ha\ing  one  end  c< 'V- 

Experiment  .  .  '  ,  ,    .    , 

with  the  string     crcd   bv    a   piccc   of    parclimcnt,    tlirouiii'i    wnicli 

telephone.  '  .  .  ,   .  ,    . 

pas>es  a  connectmg  strmg.  Words  wlusjxTcd  m 
one  tu])e  will  be  carried  to  a  considerable  distance  through 
the   string,   and   will   reach   the   ear  of   the  listener,   jilaced   at 


SOUMJ.  .IND  ITS  RliLATIOX  TO  MUSIC  17 

the   outer   end   of   the   other   tube,   with   almost   unchminij-^ed 
intensity. 

In  free  air,  sound-vibrations  sometimes  travel  to  very  great 
distances.  Instances  are  narrated  of  occasions  when  tre- 
mendous explosions  have  been   heard   for   from 

-  ,  ,  ,      .  •  .  Travelling 

tive  hundred  to  seven  hundred  and   nftv  miles,    power  of 

1      •  1111  1  1     ■         1  r  •  •"  sound. 

it  is  probable  that  the  earth  itself  assists  m  carry- 
ing these  vibrations;  l)ut  Chladni  (1756-1827)  tells  of  hearing 
the  sound  from  meteors  the  bursting  of  which  indicated  that 
the\-  were  a  hundred  and  twenty-five  miles  in  altitude.  The 
amount  of  air  affected  bv  even  slight  sounds  is  sometimes 
enormous.  Darwin  speaks  of  crickets  whose  stridulations  can 
be  heard  at  night  for  the  distance  of  a  mile.  In  such  a  case,  it 
is  calculated  that  from  five  to  ten  million  tons  of  matter  are 
affected  by  the  noise  produced  bv  an  insect  w^hich  weighs  about 
a  quarter  of  a  pennyweight! 

But    sound    rarely    travels    far    without    encountering    some 
obstacle ;  and  we  now  proceed  to  investigate  what  then  hap- 
pens.    Sound  is  found  to  be  subject  to  the  same    ^aw  of 
laws    as   are   light   and    radiant   heat,    in   that   it    reflection. 
sufTers  partial  or  total  reflection.     Let  a  sound   produced  at 
A   (Fig.  10)   strike  the  reflecting  surface  D  E  2.t  the  point  B. 

making  with  it  the  angle  .'/  B 
/:.  The  sound-wave  wmU  re- 
bound in  the  direction  of  C, 
and  the  angle  C  B  D  will  be 
equal  to  the  angle  .  /  B  E,  fol- 
^'^'  ^°"  lowing  the  law  that  the  angle 

of  incidence  is  always  equal  to  the  angle  of  reflection. 

To  demonstrate  this  law,  take  two  long  glass  or  cardboard 
tubes  .1  B.  and  arrange  them  as  in  Fig.  11,  with  a  flat  card 
placed    as    a    reflecting    surface    at    C.      Put    a    „         ,   ,. 

I  o  Demonstration 

watch  in  the  end  of  tube  .1.  covering  the  open-    °f  t^^'s  law. 
ing  with  cloth  so  that  the  ticks  are  muffled.      Ijy  listening  at 
B,  it  will  be  discovered  that  the  ticks  are  loudest  when  the 


18 


SOUND,  AND  ITS  RELATION  TO  MUSIC 


law  of  incidence  and  reflec- 
ion  is  coni])]ied  with.  Sub- 
stitute other  surfaces  for 
the  card,  and  compare  their 
reflective  power.  Xote  that 
even  a  flat,  or  fish-tail,  gas- 
flame  will  produce  good 
results.  P'g-  ''• 

The  sound-wave,  meeting  a  fiat  surface,  immediately  changes 

its  course,  and  travels  as  thotigh   it  came   from   the  opposite 

tlirection.      In    h'ig.    12,    the    wave,    striking   the 

Progress    of   a  .^  ,       ^ 

sound-wave    in     surface  .  /  B  at  right  angles,  returns  as  if  it  had 

reflection.  .     .  ^,    "  ,      \  •        ,  ^^      r 

ongmated  at   U  ;  and   the   smgle   rav   O   I   pro- 


ceeds towards  M,  where  it  is  heard  as  though  coming  from  O' 

Curved  mirrors,  like  those 

at  .1/  and  .1/'  ( Mg.  13).  have 

the  ])r()pcrt\'  of 

Experiments 

with    curved  rCUCCtrng      par- 

mirrors. 

allel  rays  of 
either  light  or  sound  to  a 
single  point  called  the  focus, 
nr,   converselv.   of   reflecting    |i  Fis.  n. 


SOUND.  AXD  ITS'  RRLATIOX  TO  MUSIC  19 

the  rays  from  this  focus  in  parallel  lines.  If  a  watch  be 
suspended  at  the  focuo  /■  of  the  mirror  .1/  (  h  ig.  13),  and  the 
l)arallel  rays  of  sound  reflected  from  .1/  be  concentrated  on 
the  mirror  .1/'.  the  ticking  of  the  watch  will  be  heard  distinctly 
at  the  focus  /'"',  sometimes  as  far  as  two  or  three  hundred 
feet   from  the  watch. 

Sound-reflection  explains  the  familiar  i)hcnomenon  of  the 
ccJu).  Objects  having-  flat,  plane  surfaces  are  best  adaj^ted 
for  this  reflection;  and  according  to  the  distance    „, 

•^  Phenomenon 

from  the  speaker  will  thev  gi\'e  back  one  or  ukm-c  °^  '^  '^'^^°- 
s_\-llal)]es.  An  oljject  distant  about  110  feet,  for  instance,  will 
return  one  syllable  onl\'.  while  an  object  distant  220  feet  will 
return  two  s}'llables.  one  330  feet  away  three  syllables,  and 
so  on.  If  these  echoes  themselves  hit  other  reflecting  surfaces, 
a  second  echo  is  produced,  and  sometimes  this  process  is 
repeated  as  long  as  the  vitalitv  of  the  sound  la-^ts.  The  result 
is  a  series  of  reverberations,  such  as  those  in  the  cry])t  of  the 
Pantheon  at  l^aris.  Cases  are  cited  where  an  echo  has  repeated 
the  same  sound  as  manv  -as  fortv  times.  Mountainous  regions, 
notablv  the  canons  of  the  Rock  Mountains,  are  especially 
suscei)tible  to  echoes.  In  large  domes,  like  those  of  St.  Paul's 
in  London  or  the  Capitol  at  Washington,  the  phenomenon  of 
"whispering  galleries"  is  frequently  displayed.  Conversations 
ma\-  be  carried  on  in  these  l)v  two  persons  cl()se  to  the  wall 
on  opposite  sides  of  the  dome,  which  are  inaudible  to  others 
only  a  short  distance  away.  Idiis  effect  is  generally  ascribed 
to  a  multiplicity  of  cross-reflections;  although  some  physicists 
assert  that  the  sound-wa\-es  under  these  conditions  are  not 
reflected,  but  run  along  the  wall,  just  as  water- wa\'es  follow 
the  outline  of  a  l)ank  when  they  strike  it  at  a  small  angle. 

When  sound-waves  are  reflected  by  surfaces  onl_\-  a  few  feet 
away  from  their  origin,  the  tendency  is  to  produce  confusion. 
If  the  pulses  of  densitv  e.xacth'  or  nearlv  coin-    „  .    ,■ 

'  ...  Kenection    at 

cide  in  sounds  thus  mo\ing  in  opposite  directions.  ^'^°'''  distances, 
the  result  is  an  increase  in  intensity;  but  if  the  condensation> 
of   the   original    sound   coincide    with    the    rarefactions    of    its 


20 


SOUXD.  .IXD  ITS  RELATIOX  TO  MUSIC 


echo,  the  result  is  a  neutralization  of  both,  and  a  consequent 
obliteration  of  the  sound    (page  41). 

Considering,  therefore,  the  manifold  j)ossibilities  for  con- 
flict of  reflections,  it  is  not  surprising  that  the  acoustics  of 
.         .        ,        concert-halls  present   ])roblems  which  have  thus 

Acoustics    of  '  i 

concert-halls.  fj^j-  proved  iusoluble.  For  musical  purposes,  a 
certain  amount  of  sound-reflection  is  necessary  in  order  to 
ffive  life  to  the  tones;  but  unless  this  reflection  l)e  admirably 


Fig.    14. 


adjusted,  confusion  will  occur  in  certain  parts  of  the  audi- 
torium, or  a  silence  co)ie  may  exist,  such  as  that  depicted  in, 
Fig.  14.  In  halls  which  have  confusing  echoes,  resort  is 
frequentlv  had  to  deadening  draperies,  or  to  wires  so  stretched 
as  to  disperse  the  conflicting  sound-waves. 

Let  us  note  that  the  resonance  of  the  reflecting  object  some- 
times afi:'ects  quite  decidedly  the  quality  and  power  of  the 
^  echoed    sound,    and    occasionallv    also    its    pitch. 

Kesonance    as    a  •-  ' 

factor  in  echo.  Discussiou  of  this  phenomenon  is  reserved  for 
Cha])ter  \'I. 

That  a  flat  gas-llame    (page   79)    ma_\'  also   reflect   sound   is 

onlv  an  instance  of  an  effect  which  may  be  produced  by  any 

gas   or   even    an}-    air-current    of    a    temperature 

Reflecting  different    from   that   of   the    surrounding   atmos- 

power   of  gases 

and  air-currents,    plierc.      The    rc verbcratiou    of    thunder    is    thus 

rog    signals.  ' 

caused  not  onlv  b\-  echoing  clouds  and  solid 
obiects,  but  also  by  varying  currents  of  heated  air.  Tyn- 
dall  proved  In-  an  elaborate  series  of  experiments  that  air- 
currents    were    responsible    for    the    great    variation    in    the 


SOr.M),  .IXD  ITS  Rl-LATIUX  TO  MUSIC 


21 


distances  at  which  tOg-sij^nals  could  Ijc  lieard  on  different 
occasions.  Sometimes,  owing  t(j  these  invisiljle  reflectors,  the 
signals  could  he  heard  onl\'  a  short  (hstance  on  a  perfectly 
clear  day  ;  while  at  other  times,  when  the  air  was  filled  with 
moisture,  the  distance  which  the  sound  traxelled  was  >uri)ris- 
ingl\-  great.  The  loudne>s  of  sounds  at  night,  too,  is  largely 
caused  hv  the  ahsence  of  the  air-currenls  which  are  more  likel_\- 
to  occur  during  the  da}'  time. 

Speaking  trumpets  and  ear  trumpets  involve  ])ractical  appli- 
cations of  the  laws  of  reflection.  In  the  former  (  I^lg.  15), 
the  sound  in  emerging  is  conx'crted  into  parallel    ^      i-  ^ 

•^       '^  1  speaking    and 

ra\s.      just   what   part  the  hell-sha])ed  end   i)lays    ^^r  trumpets. 

in     producing     this 

result    is    not    well 

known.     In  the  ear 

irtniipct  the  re\-erse 

^'°-  ^^-  process  takes  ])lace. 

since  the  waves  from  the  outer  air  hecome  reinforced  in  the 

tuhe   of   the    instrument,    and    thus    reach    the    ear    in    greater 

vf)lume. 

Sound,  like  light,  dex'iatcs  from  its  cour-e  w-hcn  it  enters 
a  medium  of  difl:'ercnt  den-ity.  This  phenomenon  is  called 
refraction.     In  an  a])i)aratu>  designed  hv   Sond-    .^ 

-  Demonstration 

haus    (1815-18X6),   shown   in    I^g.    16.   carhonic-    of  refraction. 

acid  gas  forced  into  a  rul)])er  hag  J,  wdiich  is  supported  in  a 

Ijroad  hrass  ring 
0  ()'  gi\es  the  bag 
the  form  of  a  dou- 
hle  convex  lens.  We 
c  a  n  demonstrate 
the  fact  that  a 
sound  })roduced  at 
.S'  comes  to  a  focu< 
just  below  B  by 
strewing  sand  on  a 
membrane     at     the 


22 


SOUXD,  AXD  ITS  RELATION  TO  MUSIC 


B>  ! 


i  ! 


to])  of  the  box  B,  since  the  sand  will  dance  about  under  the  in- 
fluence of  the  sound  when  the  lens  is  present,  but  will  remain 
quiet  when  the  lens  is  removed.  1  he  focusing  takes  place 
b  e  c  a  u  s  e   t  h  e  /  ^ 

sound-waves,  on 

entering   the  ,  ,  '^ 

denser  gas.  be- 
come flattened, 
and  when  they 
emerge  the  por- 
tion o  f  the 
waves  at  the 
edges  thus  come 
to  precede  the  interior  portion,  as  in  I""ig.  17.  hnallv  concen- 
trating at  B. 

When  a  large  object   intervenes  l^etween   a   sound   and   the 

auditor,  the  soimd  loses  in  its  intensity,  and  it  mav  be  quenched 

,   ,    ,  entirelv.  if  the  object  be  of  sufficient  size.     The 

Sound-shadows  -  •' 

and  diffraction,  name  of  somidshadoic  has  been  applied  in  this 
decrease.  l)Ut  if  the  o])posing  object  be  small,  the  sound-waves 
are  bent  around  it.  just  as  the  water-waves  dash  around  a  small 
rock.  This  phenomenon  is  called  diffraction.  In  cases  of  tre- 
mendous explosions  of  dynamite,  it  has  been  found  that 
windows  on  all  sides  of  houses  in  the  path  of  the  sound-waves 
were  forced  in  :  a  result  which  is  explained  by  this  proj^erty 
of  sound.  If  we  listen  to  a  railroad  train  as  it  dashes  through 
tunnels  and  behind  hills,  the  different  grades  of  the  sound- 
shadows  will  be  apparent. 


SOUND,  AND  ITS  RELATION  TO  MUSIC  23 

SUMMARY 

SoiTNH  travels  in  air  at  the  rate  of  1090  feet  per  second 
vvhen  the  temperature  is  at  the  freezing  point,  and  one  foot 
faster  per  second  for  each  degree  of  rise,  Fahrenheit.  I  he 
velocity  is  tlie  same,  whatever  he  the  densitv  of  the  air. 

Sound-velocitv  varies  much  in  its  rate  in  other  media.  In 
metals  and  wocxls  it  is  several  times  as  great  as  indicated  in 
the  ahove  figures. 

Together  with  light,  sound  possesses  the  power  of  reflection, 
refraction    and    diffraction. 

In  reflection,  the  angle  of  incidence  is  always  equal  to  that 
of  reflection.  Reflection  gives  rise  to  echoes  and  reverbera- 
tions. Smooth  surfaces  and  even  gases  and  air-currents  are 
good    reflectors. 

By  refraction,  sound-w'aves  can  be  driven  from  their  course, 
and  brought  to  a  focus. 

In  diffraction,  sound-waves  are  bent  around  objects  of  small 
size.  When  the  opposing  object  is  sufficiently  large,  a  sound- 
shadow  occurs. 

REFERENCE   LIST. 

Tyndall,  Chapters  1.  5,  7. 

Zalivi.  Chapter  3. 

Catchfool.  Chapters  3,  8. 

Harris,  Chapter  2. 

Blaserna,  Chapter  2. 

Stone,  Chapter  2. 

Laz'ignac,  Chapter  1,  B. 

Poynting  ami  Tho})ipson,  Chaptei*  2'. 

Barnes.  Chapters   10,   11 

Barton,  Chapter  10. 

Broadhouse,  Chapter  2. 

Taylor,  Chapters  1  and  7. 


CHAPTER  III 

As  we  walk  along  a  cc)untry  road  and  flirect  our  attention 

toward  the  various  sounds  wliich  reach  our  ears,  we  can.  as 

a  general    ru;e,   draw    fairl\-   accurate   inferences 

Inferences   from  ....  .         ' 

different  as  t(j  tlieir  ongms.      We  conchide  that   a  shrill. 

sounds.  .     .  . 

pipmg  note  is  produced  hy  a  hird  i)erched  on  a 
near-h\-  tree,  and  that  the  low.  droning  sound  conie>  from  a 
distant  waterfall.  Another  low.  hut  more  rasping  sound  he- 
tokens  the  ])resence  of  a  -aw-nhll  :  and  from  its  direction  and 
degree  of  intensit\-  we  assign  it  a  position  clo-e  to  the  water- 
fall. 

Since  we  are  immediateU-  ccmscious  of  the  acuteness  of  the 
bird-note.<  as  compared  with  the  gra\'itv  of  the  tone  of  th.e 
~,  ..      waterfall,  we  distingui-h  between  the  two  >ounds 

ihree    properties  ' 

°^  sounds.  priiuarily  h\-  their  dilTerence  in  pitcii.     I'-ut  Ijefore 

we  can  separate  the  tone  of  the  waterfall  from  thai  of  tlie 
saw-mill,  we  must  note  their  ditterence  in  qiialitx.  since  their 
pitches  are  nearl\-  alike.  h'inall_\\  we  conclude  that  the  hirrl  is 
clo-e  at  hand,  hut  that  the  other  two  objects  arc  a  nhle  (.»r  mcjre 
awa_\\  froiu  the  pro]iortional  hniducss  with  \\hich  the  indi- 
vidual >ounds  reach  us.  d"he>e  illustrations  are  cited  a>  ex- 
amples of  the  three  ])ropertics  of  pitch.  Icita'ncss  and  (luality 
which  all  >ounds  ]xjs>ess.  and  which  we  now  ])roceed  to 
investigate. 

Referrmg  to    b'ig.   .^    '  r'agf  h\    we   recall   that  the   \-ibration> 

of  the  metal  bar  were  distinguishable,  licfore  the\-  produced  a 

tone.      \\  hen    the   Itar   wa<   sutticienih-    >hortened 

Pitch   fiependent       .  .   ,       . 

on   vibration  trif  the  oscillations  to  gi\'c  out  a  souud.  iK.nvever, 

number,  .  .    '  ,       .       .         . 

the  toriuer  were  ^-o  fast  that  thev  ki-t  tiieir  md;- 
A'idualit}' :  and,  a-  the  bar  was  further  .shortened  and  the  :-ou!id 
con>e(|ueinl\-  rij-e  in  ])itch,  the  \ibrati(jns  Ijlended  together 
comjdetel}  .      Similarh'.    if    a    violin    strmg    be    plucked    in    the 


SOUND.  AND  ITS  RllLATION  TO  MUSIC 


25 


middle,  the  whir  of  its  vibrations  is  visible ;  but  when  the 
string  is  shortened  and  the  pitch  accordingly  rises,  these 
vibrations  are  seen  to  be  much  accelerated.  From  numerous 
experiments  of  this  character,  it  has  been  proved  that  the 
pitch  of  a  sound  depends  on  the  number  of  vibrations  of 
the  sounding  body:  if  these  increase  the  pitch  rises,  and  if 
they   decrease   the   pitch   falls. 

To  determine  the  exact  number  of  vibrations  which  a 
sounding  body  makes  per  second,  a  number  of  devices  have 
been    employed.      The    distinguished   astronomer         . 

.  .  Devices    for 

(ialileo    (1564-1642)     found    that    in    passing    a   determining  the 

.  number    of 

knife-blade   over   the    milled    edge   of    a    com    a    vibrations. 

.  .  Savart's   Wheel. 

sound  was  produced  which  rose  m  pitch  as  the 
knife  moved   faster.     A  machine  for  measuring  sound  based 
upon  this  princijile  was  invented  by  Savart   (1791-1841).     As 

shown  in  V\g.  18, 
this  consists  of  a 
cog-wheel  B, 
which  can  be  ro- 
tated rapidly  by 
means  of  the  wheel 
./,  connected  with 
B  by  the  l)elt  D. 
Fig.   18.    savarfs  Wheel.  If  a  Card  be  placed 

against  the  cogs  at  7:  and  the  wheel  turned  slowly,  a  tap  is 
heard  each  time  that  a  cog  releases  the  card.  With  an  increase 
in  c[uickness  a  M)und  is  heard;  and  b_\-  noting  the  number  of 
revolutions  of  B  per  second  and  multiplying  this  by  the  num- 
ber of  cogs  on  the  wheel,  the  \'ibrati<jn  number  of  this  sound 
is  obtained.  If  it  l)e  desired  to  ascertain  the  pitch  of  another 
sounding  ol)ject.  such  as  the  tuning-fork  C.  the  velocity  of 
the  wheel  is  regulated  so  that  the  pitches  of  the  two  sounds 
coincide,  when  the  process  just  described  will  give  the  desired 
result. 

Another  instrument,  which  produces  sound-vibrations  by 
means   of   putts  of   air.   is  the   invention   of   Cagniard-Latour 


26 


SOUND.  .IXD  ITS  RELATIOX  TO  MUSIC 


Latour's 
siren. 


1^1777-1859).  and  is  called  the  siren    (Fig.   19). 

In  this,  a  disk  .s"  jr.  having  a  circular  row  of 
holes,  revolves  o\"er  a  plate  similarly  perforated.  This  latter 
ulate  form->  the  top  of  a  hollow  chest  A  .-/.  from  which  wind, 


Fig.    19.     C;i.t;n:iir(l-I.,.itonr's  .siren. 

entering  through  the  tnhe  B  B.  is  forced  in  puffs  that  are 
emitted  simultaneotisly  from  all  the  holes.  \vhene\'er  these 
coincide.  Tims  if  there  he  twelve  holes,  as  in  the  drawing, 
e\'identl\-  twel\"e  of  these  comhined  ])utfs  nuist  occur  at  each 
revoltition  of  the  disk.  The  holes  are  cut  slant-wise  in  opjK^ 
site  directions,  as  sliown  in  the  lower  right-hand  drawing, 
which  is  a  section  throtigh  //  //  in  the  ujjper  right-hand  figure. 
\'>y  this  means  the  stream  of  air  is  made  to  turn  the  disk,  as 
well  as  to  ])ro(lttce  the  sotmd-jmffs.  A  screw  thread  /  moves 
a  meclianism   which   registers   the  results  on  a  dial  .■:  c. 

When  the   instruiuent   i<   set    in   motion,   tlic   di^k.   revolving 


SOUND,  AND  ITS  RELATION  TO  MUSIC 


27 


slowly  at  first,  gives  out  a  series  of  detached  puffs      As  these 
quicken,  however,  a  low  sound  is  heard,  which    ,,       .  ,, 

'  '  '  '  Use    of   the 

rapidly  rises  in  pitch.  To  test  the  number  of  s'""^"- 
vibrations  of  any  other  sounding  body,  therefore,  the  siren 
must  be  made  to  gi\e  out  a  constant  tone,  in  unison  with  the 
one  that  is  tested,  just  as  was  the  case  with  Savart's  wheel; 
and  the  frequency  is  then  announced  on  the  dial.  With  both 
of  these  instruments,  however,  the  difficulty  con- 

,  .  .  .      ,  .  ,  Difficulties    in 

sists  m  keepmg  a  given  pitch  constant,  since  the   connection 
slightest  deviation   from  this  constantlv  vitiates 
the  results.     Helmholtz  partly  remedied  this  defect  by  using 
an  electric  motor  to  run  the  siren,  in  place  of  the  irregular 
wind   supply. 

A  graphic  method,  which  is  capable  of  giving  very  accurate 
results,  employs  a  style  attached  to  a  tuning-fork,  as  in  Fig. 
3     (page    3),    except    that    the    tuning-fork    is    .^^^    ^^  ^^^ 
made  to  write  its  story  upon  a  revolving  drum   method. 
T  T,  shown  in  Fig.  20.     This  drum  is  turned  by  the  shaft 
A   b.     After  the  drum   has  thus  been   kept   in  motion   for  a 


Fig.   20. 


28  SOUND,  AND  ITS  RELATION  TO  MUSIC 

given  time,  say  two  seconds,  the  number  of  vibrations  recorded 
during   this   time   mav    easily    be   counted. 

Scheibler  (1777-1837)  made  an  instrument  called  the 
tonometer,  consisting  of  a  series  of  tuning-forks  the  vibra- 
c  ,   -. ,    ,  tions    of    which    differ    bv    a    small    and    eriual 

bcneibler  s  -  ' 

tonometer.  number,  through  the  compass  of  an  octave.     In 

order  to  test  a  given  pitch  by  means  of  this,  it  is  onl\-  neces- 
sary to  compare  it  with  the  tuning-fork  nearest  in  unison 
with  it.  Koenig  afterward  constructed  on  this  ])]an  a  (/rand 
tonomctre  iDik'ersal,  which  covered  the  entire  range  of  au<lible 
sounds,  and  involved  a  hundred  and  fifty  tuning-forks,  ad- 
justed with  the  utmost  nicety,  of  which  the  largest  were  five 
feet  in  length. 

These,  represent  only  a  few  of  the  devices  used  in  pitch- 
measurement.  Others  include  modifications  of  these,  and 
^,,  instruments  constructed  on  dift'erent  lines,   such 

Other 

methods.  jjg    thosc    involving    strings     (page    33).      With 

these  varied  means  for  verifying  results,  it  is  evident  that  pitch 
can  be  calculated  to  a  high  degree  of  minuteness. 

As  to  the  exact  limits  of  audible  sounds,  scientists  are  not 

fully  agreed.      Some  assert  that  the  limit  of  grave  sounds  is 

fifteen  or  sixteen  vibrations  per  second.     Ilelm- 

The    limits  111  1      1       1 

of  audibility—      boltz,   howcvcr.   Contended   that  no   true   tone   is 

grave     tones.  ,,,.,.  .     ,  .  , 

produced  by  vibrations  of  less  frequency  than 
thirty  per  second;  and  it  is  probable  that  this  view  is  correct, 
although  for  practical  purposes  the  theoretical  limit  of  six- 
teen is  frequentlv  assumed.  To  some  ears,  moreover,  sciuncU 
are  perceptible  at  a  lr)wer  limit  than  to  others;  and.  also,  the 
difference  in  the  composition  of  the  sounding  bodv  may  cau^e 
a  difference  in  the  number  of  vibrations  necessary  to  blend 
into   a   tone. 

Of  acute  sounds,  the  limits  of  audibilit\'  arc  much  more 
difficult  to  fix.  It  is  asserted  that  sounds  of  which  the  \"ibra- 
M  ,     ,  tion    number    is    as    high    as    38,000    per    second 

Measurement    of  &  i 

acute  sounds.  have  been  heard  ;  but  for  most  persons  the  limit 
is    about    IT). 000   vibrations.      For    the    measurement    of    verv 


SOUND.  AND  ITS  RELATION  TO  MUSIC  29 

high  pitches  the  whistle  shown  in  V\g.  21   has  been  devised, 
which  is  capable  of  adjustment  to  the 
slightest  variation  in  acute  pitch.    The 
air  is   forced  into  this  by  the   rubber 
'^'g-  21-  bulb,    and,   l)y   means   of    a    scale   at- 

tached to  the  whistle,  the  vibrating  column  of  air  in  the  tube 
can  be  shortened  as  minutely  as  1 /250th  of  an  inch. 

Young  people  are,  in  general,  ca])able  of  hearing  sounds 
of  a  much  higher  pitch  than  is  perceptible  to  those  of  maturer 
vears.     Likewise  the  degree  of  suscei)tibilitv  to 

' ,.  ~,  .      ,  .  .,.,..,',         Differences   in 

ditrerent  pitches  varies  largel\-  with  individuals,    susceptibility 

,  .  ...  ,  '       ■  ,  ,  to   pitch. 

\  ery  high  or  very  low  sounds  are  harder  to 
ditTerentiate  than  those  of  medium  pitch.  Sometimes  even 
the  trained  ears  of  a  piano  tuner  are  incapable  of  adjusting 
the  pitches  of  the  notes  in  the  uppermost  octave  with  accuracy. 
Occasionally,  also,  we  discover  a  "tone-deaf"  person,  who 
finds  difficulty  in  distinguishing  between  contiguous  sounds 
in  the  middle  musical  register,  especiallv  if  these  be  given  out 
by  a  non-sustaining  instrument,  like  the  piano.  Such  obtuse- 
ness  to  pitch  mav  generallv  be  remedied,  in  part  at  least,  by 
sufficient  cultivation,  especiallv  in  early  youth  :  a  result  which 
speaks  for  the  desirability  of  ear-training  courses  in  our 
schools. 

To  a  few  individuals  is  given  the  facultv  of  what  is  called 
"absolute  pitch,"  which  means  the  power  of  immediately  rec- 
ognizing  the   i)lace    in    the    scale    of   anv    sound     .,     ,  ^ 

f  *>  '  '  Absolute 

heard.  Prima  facie,  one  possessing  this  gift  p'^*^^- 
should  have  other  qualities  of  a  musician  :  although  this  result 
does  not  always  follow,  just  as  absolute  pitch  is  not  by  any 
means  an  universal  or  even  a  common  possession  of  musicians. 
Since  our  system  of  notation  employs  the  same  letters,  from 
A  to  G  inclusive,  for  each  octave,  it  is  necessary  to  indicate 
more    specificallv    which    octave    is    meant    when 

f       ,  ,"  ...  ,.-,..  Distinguishing 

one    ot    tliese    letters    is    designated.      Scientists    names  of  the 

octaves. 

use  the  signs 

C_2,   C-i,   Ci,   C,,   Cs,   C4,   C5.   Co,   C7,   &c.. 


30  SOrXD.  .-IXD  ITS  KHLATIOX  TO  MUSIC 


o 


f  which  C ^  is  the  treble  C  '^-°^^.  and  the  others  are  the  Cs 


in  both  directions  from  this,  at  octave  distances.  A  system 
more  commonly  cmployerl  by  musicians,  and  the  one  which 
\ve  >hall  u>e  in  our  discussi(Mis.  designates  the  scale  notes  as 
follows  : 

Two-lined  Three-liired 


D   K 


Still  lower  octaves  are  indicated  bv  adding  figures  below  the 
capital  letter-  (C,  ^n^'  '^""-^  higher  ones  by  adding  to  those 
ab(.)ve  the  small  letters  (  c"'.  c''.  c\;c.  ). 

.\>  jiitch  can  be  measuredi  so  accurately,  one  would  expect 
that  the  advantages  of  an  uni\-ersal  standard  would  cause  the 
„,  immediate  a(k)i)ti(in  of  such  aii  one   for  all  i)ur- 

rluctuating  '  ^ 

pitch-standards.  |„,^es.  I'.ut  tlic  facts  sliow  f|uite  Contrary  con- 
ditions. a>  will  be  understood  b\-  consulting  the  table  on  the 
oppo-iite  ])age.  which  indicates  some  of  the  fluctuations  of  the 
pitch-standard  since  tlie  \"car  1  oOO.  .V  o\'er  the  lirst  colunm 
shows  tile  rise  in  ])itch  fri^m  the  ideal  bjwest  in  ,-emitones  and 
hundrecltlis  of  semitones,  while  tmder  (/'  in  the  second  colunm 
are  gi\'en  the  numi)er  of  \il)rations  of  a'  in  the  stated  cases. 
Owing  chiefl\'  to  the  de.-ii"e  of  leaders  of  bands  and  orchestras 
to  produce  ])rilliant  etlecl-.  the  jiitch  ha>  gradtiallv  risen  frcim 
the  time  of  Ilandel  and  Mozart,  so  that  ncjw  singers  are  com- 
pelled to  render  compo>ilion-  of  that  jx'riod  more  than  a 
semitone  lugher  than  was  originalK-  iniendcd.  to  the  disad- 
vantage of   boih    singer   and   coni])o>ition. 

A   number  of   attem])ts   ha\-e   l)een   made   in   recent   \ears  to 
secure   uniformitw      As   the    result   of    -everal    con\-entions   of 
piano   an<l   organ    manufacturers,    most   of    these 


Modern 
standards 


nistrument: 


ai'e     now     lunerl     to     the     so-called 


hitcrnati(>}ial  /'itch,  identical  with  llie  f'rench  Diaf^ason  >ioniia! 


SOrXD.  AXD  ITS  RliLATIUX  TO  MUSIC  31 


u        X 


■f.rr-Z.r.-r- 


■  O  —  'n  —  X 


■f.'ij'Z    ■  s'  / 


t:  •/.     '-  '-^.  '^^    [       ^ 


XX  -  o  c 


X  X  t^  OC  X 


vi    s  £  -     - : 


---     -^J- 


-r  4  -T  -T  ir.  in       1 ,  X  '—  .£  o 

-r  -r  -T  T  -r  -r         t  -^  ir,  .o  ir. 

'J-    C   ~  1  "".  "-.   r  ;      ->   -T  I      -TOO 

r--;  -^  rW  (^  '^  -^'  !     V  T  '     iy-i  r^'  r^ 


32  SOUND,  AND  ITS  RELATION  TO   MUSIC 

of  1859,  which  has  a'=435.  ^lodern  orchestras  and  mihtary 
bands,  however,  generally  employ  the  higher  Schcibler  Stutt- 
gart pitch  of  1834,  by  which  a  has  440  vibrations.  Physicists, 
for  the  sake  of  ease  in  computations,  take  as  pitch-basis  the 
theoretical  limit  of  audibility,  giving  C  =16  vibrations,  so  that 
Q^32,  C=i64.  r=128,  and  c'=^256  vibrations.  From  these 
figures  o'=426.6,  a  standard  considerably  lower  than  either  of 
those  just  cited. 

In  the  earlier  centuries  of  the  Christian  era,  when  music  was 
almost  exckisively  vocal,  the  tones  employed  were  restricted 
„,  .    ,         to  fifteen  or  twenty,  arranged  diatonically  in  the 

The    musical  .'  '  fe>  .; 

compass.  middle  register  (page  94).     With  the  advent  of 

chromatic  notes,  however,  and  with  the  greater  latitude  which 
followed  the  extended  use  of  instruments,  the  compass  rapidly 
increased  until  it  finally  embraced  all  the  tones  from  the  limit 
of  audibilit}-  in  the  direction  of  grave  sounds  to  those  sounds 
which  are  so  piercingly  acute  as  to  be  unavailable  for  artistic 
purposes.  The  ])iano  now  begins  with  .1  of  about  27^> 
vibrations,  and  continues  to  c^'  of  4224  vibrations.  In  the 
orchestra  the  lowest  note,  rendered  by  the  contra-bassoon,  is 
C  of  about  33  vibrations,  while  the  highest  is  <i^'  of  the  piccolo, 
with  4752  vibrations. 

Allusion  has  been  made  to  the  influence  of  wind  u])on  sound- 
velocity.     While  the  sound-waves  are  pushed  forward  by  the 
wind  when  both  are  travelling  in  the  same  direc- 

Influence    on  .  .  .  , 

pitch  of  wind        tion,  the  resultant  pitch  is  not  affected,  as  nfight 

and   intensity. 

l)e  expected,  smce  the  sound-waves  are  at  the 
same  time  elongated  so  that  eventually  the  same  number  reach 
the  ear  in  a  given  time  as  would  do  so  under  normal  conditions. 
Likewise  the  intensity  of  sounds  has  no  effect  whatever  on 
their  pitch,  ff)r  otherwise  the  music  of  a  band,  produced  by 
instruments  of  varying  strength  cjf  tone,  would  sound  hope- 
lesslv  out  of  tune. 

If,  however,  the  distance  between  a  sounding  body  and  the 
listener  varies  rapidl\-.  a  perceptible  alteration  in  pitch  results. 
§ince,   when   the   object    is   approaching,   the   sound-waves   are 


SOUND,  AND  ITS  RELATION  TO  MUSIC  33 

crowded  together,  and  when  it  is  receding,  the  number  which 
reacli  the  Hstener  in  a  given  time  is  correspondingly  reduced. 
Thus    the   whistle   of   an   engine    becomes   more    ^  „  c 

■=•  Influence  of  a 

acute  when  the  train  rushes  towards  us,  and  falls   ■"^'p!^.  change  of 

'  position    upon 

gradually,  after  it  has  passed.  p'*'^'^- 

Instrument  makers  must  take  into  account  the  laws  which 
govern  pitch,  in  order  to  utilize  their  materials  to  the  best 
advantage.     For  the  study  of  such  laws,  an  in-    ^.     , 

■^  -^  _  '  The    laws    of 

strument  called  the  sonometer  is  especially  valu-    P'^<^h. 
able.     Pythagoras,  the  Greek  philosopher,  used 
this  under  the  name  of  monochord,  or  instrument  of  a  single 
string ;  and  from  his  time  to  the  present,  scientists  have  found 

it  one  of  the 
most  available 
means  of  inves- 
tigating tonal  re- 
lations. In  its 
modern     form 

Fig.    22.     Sonometer.  (  Fig.  22  )    it  COn- 

sists  of  a  long  resonant  box  of  fir,  M  N,  over  which  are 
stretched  two  wires.  One  of  these  a  d  is  attached  to  a  pin  at 
each  end,  and  can  be  regulated  in  its  tension  bv  a  piano  key, 
p.  The  second  string,  b  R,  is  fixed  at  one  end  only,  since  the 
other,  passing  over  the  pulley  R,  is  stretched  by  a  weight  at  P. 
The  bridges  B  and  B'  are  stationary,  while  the  bridge  C  moves 
upon  a  scale  divided  into  millimeters. 

If  the  bridge  C  be  removed,  and  one  of  the  strings  be  plucked 
in  the  middle,  it  will  vibrate  in  its  entire  length,  and  give 
out  a  fundamental  tone.     Let  the  bridge  be  now    Laws  of 

1  1  1  •  •         1-     •  1      1     •  strings. 

msertcd   so  that  the   strmg  is   divided   into   two    i.  That  con- 

,  T-       1  r-      1  -11        •  cerning  the 

equal  parts.  Fach  ot  these  will  give  a  tone  an  length, 
octave  above  the  original,  and  will  vibrate  twice  as  fast.  In 
like  manner,  if  the  string  be  divided  into  three  equal  portions, 
each  of  these  will  vibrate  three  times  as  fast  as  the  entire 
string;  and  one  of  four  equal  portions  will  have  four  times 
the  original  vibration  number.     Thus  the  number  of  vibrations 


34  SOi'Xl).  .1X1)  ITS  RBLATIOX  TO  MUSIC 

incrca>es  in  exact  proportion  as  the  string  is  sh(jrtene(l,  or,  in 
mathematical  terms,  the  number  of  vibrations  is  in  inverse 
proportion  to  the  length  of  the  string. 

Let  us  next  make  the   weight   P  e(|ual   to  one   jjound.   and 

a-ccrtain  the  viljration  number  of  /'  K  at  this  tension.      If  we 

then  increa>e  the  weight  until  this  \'ibrati(>n  num- 

cerning  the  i)er  is  (loul)ie(l.  wc  shall  tind  tl'ic  weight  cciual  to 

tension.  .  .  .  '  •     •        i 

tour  [)ounds.  Likewise  t(j  trcijle  the  original 
sihratidii  number  requires  a  weight  nf  nine  pounds,  and  to 
qtiadruple  it  one  of  sixteen  pounds.  Therefore,  the  weight 
mu>t  e(iual  in  pounds  not  the  number  hv  which  the  original 
\ibrations  ha\-c  been  multi|)lie(I.  but  the  square  of  that  number. 
Thu-  two  times  the  original  number  C)f  \-ibrations  is  produced 
1)\-  a  weight  2x2  the  original  one,  three  times  the  original 
vibration  number  b_\-  a  weight  3x3  the  cjriginal  one.  and  so 
forth.  Hence,  coiuerseh-  stated,  the  number  of  vibrations  per 
second  of  a  string  varies  directly  as  the  square  root  of  its 
tension. 

Again,  if  the  two  strings  of  the  sonometer  be  gi\-en  the  >ame 
length  and  tension,  and  one  is  twice  as  thick  as  the  other,  the 
3.  That  con-        latter  will  \ibrate  twice  a>  fast  as  its  companion; 

cerning  the  .  .  ... 

thickness.  and.  Ill  general.  an\'  increase  m  thickness  occa- 

-i(jn.s  a  corresponding  decrease  in  the  vibration  number.  Thus 
we  ma\-  assert  that  the  number  of  vibrations  of  a  string  varies 
in  inverse  proportion  to  its  thickness. 

L'pon  these  three  laws  i>  ba-ed  the  con-truction  of  all 
stringed  instruments.  In  those  like  the  \'iolin,  where  the  strings 
^,  ,      are  few  and  the  tension-strain  is  not  great,  strings 

Observance  c-i  ^  ^ 

these  laws  in        -^n  ^^f  ^\^q  .same  length  are  u-ed,  while  their  i)itch 

instrument  '^ 

'^^'''"g-  is  regulated  by  their  thickness  and  tension.      In 

the  man\'-stringed  ])iano  and  harp,  howex'cr.  the  strain  is  made 
more  nearlv  equal  by  shortening  the  strings  as  the_\-  ascend  in 
arulenes.s,  as  well  as  b\-  diminishing  their  thickne.ss.  Thu-  the 
short  tine  wire  of  the  high  tones  is  replaced  in  the  lower  ones 
b\-  a  hea\\-  wire  several  feet  in  length  and  further  weighted  by 
:i\\  encircling  wire-coil. 


sorxD,  jxn  its  rjslatiun  to  music  35 

'I'lie  inslrunicnt  maker  must  also  remcml)c'r  that  the  laws  of 
>irings  apply  strictly  only  to  the  ideal  string  detined  b}'  physi- 
cists  as    '"a   perfectly    uniform   and    flexible    Idi-    .,   ,.^     . 

i  .  Modifications 

ment  of  solid  matter  >tretched  between  t\v(j  tixed  °^  ^^^^^  '^'^^• 
points."  As  there  are  always  imjjerfections  in  actual  strings, 
especialK'  in  the  (lirecti(jn  of  stiti"ness  and  lack  of  tmiformitx, 
the  laws  mu>t  be  somewhat  mochtied  to  suit  these  existing 
conditions.  'J"liu>.  when  a  string  is  divided  intcj  two  e(|ual 
parts,  each  of  these  will  be  found  a  trifle  flatter  than  it  should 
be  theoretically. 

( )ther  sounding  bodies  are  subject  to  laws  srimetimes  quite 
different    from   those    regtilating   the   pitch    of    strings.      With 
rods,  the  i)itch  rises  verv  rai)idh'  as  the  vibrating 
jiart  IS  shortened,  so  that  the  number  of  vibra-   vibrating 

rods  and   tubes. 

tions  IS  mversely  proportional  to  the  square 
of  the  length  of  the  vibrating  part.  1\ibes  are  subject  to 
conditions  more  nearlv  like  those  governing  <trings,  since  the 
pitch  of  the  air-vibrations  in  the  tube  varies  inversely  as 
the  length  of  the  tube.  -\  fuller  discussi(jn  of  these  law--  i> 
reserved  for  a  following  chapter. 


36  SOUND,  AND  ITS  RELATION  TO  MUSIC 

SUMMARY 

Sounds  differ  chiefly  in  respect  to  their  pitch,  loudness  and 
quality. 

Pitch  depends  upon  the  number  of  vibrations  which  a  sound- 
ing body  performs  in  a  given  time. 

The  vibration  number  per  second  of  a  sounding  body  is 
calculated  in  various  ways,  such  as  by  Savart's  wheel,  I.atour's 
siren,  the  graphic  method,  and  the  tonometer. 

Sounds  are  audible  for  something  over  eleven  octaves,  or 
from  16  to  38,000  vibrations  per  second,  although  the  sense  of 
pitch  varies  much  with  different  persons.  Of  these  sounds  only 
those  of  between  16  and  4800  vibrations  are  used  in  music. 

Standards  of  pitch  have  varied  greatly  at  different  times  and 
for  different  purposes.  Even  now  there  are  several  standards 
in  use. 

Pitch  is  unaffected  by  wind  or  loudness,  but  varies  some- 
what when  a  sounding  object  rapidly  approaches  or  recedes 
from  the  listener. 

Instruments  are  constructed  in  accordance  with  the  laws  of 
pitch,  which  have  been  ascertained  with  regard  to  the  various 
kinds  of  sounding  bodies.  Those  governing  strings  depend  on 
the  length,  tension  and  thickness  of  the  string. 

REFEREN'CE   LIST. 

HclnihoUz,  Chapter  1. 

Harris,  Chapters  4,  9. 

Taylor,  Chapter  2. 

Zahm,  Chapters  2.  4. 

Lavignac.  Chapter  1,  A. 

Stone,  Chapter  4. 

Tyndall.  Chapters  2,  3. 

Broadhouse,  Chapters  5.  9,  Appendix  C. 

Poynting  and  Tlionipson,  Chapters  3,  6. 

Barnes,  Chapters  5,  3. 

Barton.  Chapters  1.  10. 

lUascrna,  Chapter  4. 

Catchpool,  Chapter  7. 

Pole,  Chapter  3. 


CHAPTER  IV 

Loudness,  Interference,  and  Resultant  Tones 

That  the  loudness  with  which  a  sound  strikes  our  ears  is 
intimately  associated  with  the  degree  of  energy  with  which  the 
sounding  hodv  is  vibrating  is  a  matter  of  com-    ^ 

*  -  °  .  .  Relation    of 

mon  observation.      Pluck  a  violin   string  gentlv,    intensity  to 

".       amplitude. 

and  the  tone  which  results  is  weak.  Pluck  it 
harder,  so  that  it  oscillates  violently  from  side  to  side,  and  a 
strong  tone  is  heard.  Again,  strike  a  tuning-fork  lightly,  and 
observe  the  weakness  of  the  tone  which  it  gives  out.  A  harder 
stroke,  imparting  added  energy  to  the  vibrations,  will  greatly 
increase  the  sound-power.  Py  a  slight  modification  of  the 
experiment  shown  in  Fig.  3,  the  relation  between  the  extent  of 
vibration  and  the  strength  of  tone  can  plainly  be  seen.  Let  the 
smoked  glass  be  pulled  slowly  along,  after  the  tuning-fork  has 
been  agitated,  until,  decreasing  gradually  in  loudness,  the  tone 

ceases  altogether. 
A  narrowing 
white  space  on 
the  glass  is  the  re- 
sult,  as   exhibited 

Fig.  23.  i"  J^ig-  -^^-  ^^lii^'^i 

demonstrates  that 

the  width  of  the  vibrations  gradually  diminishes   as  the  tone 

lessens.     The  width  of  vibration  is  called  its  amplitude ;  and 

physicists  have   formulated  the  law  that  the  strength  of  the 

sound    varies    according   to    the    square    of   the    amplitude. 

Thus  in  the  case  of  two  tuning-forks  ./  and  B.  of  the  same 

pitch,  if  ./  vibrates  with  an  amplitude  of  one-fifth  of  an  inch 

and  B  with  that  of  one-tenth  of  an  inch,  the  sound  of  .1  will 

be  four  times  as  loud  as  that  of  B,  since  it  vibrates  through 

twice  the  distance. 

It  has  also  been  found  that  sound-vibrations  are  subject  to 

37 


38 


SOUXD.  AND  ITS  RELATION  TO  MUSIC 


the  law  which  governs  the  vihrations  of  a  pendulum,  namely. 
.      ,.    ,  that   within   ordinary    limits   the   number   of    vi- 

Amplitude  -- 

and  pitch.  brations    continues    the    same,    whatever    be    the 

extent  of  the  swing.  Hence,  increase  or  decrease  in  the 
amplitud3  of  vibration  of  a  sounding  body  does  not  affect 
its  pitch,  since  the  number  of  vibrations  remains  constant. 

In  free  air.  the  vibrations  proceed  from  the  sounding  body 
in  the  form  of  an  enlarging  sphere.  [Mathematicians  have 
^.  ,        determined  that  the  mass  of  air  included  within 

Distance    and 

intensity.  ^  yard's  radius   from  the  centre  of  a  sphere  is 

only  one-fourth  of  that  included  within  a  two  yards'  radius. 

and  one-ninth  of  that   within  a  three  \ards'   radius.      Hence. 

the  sound-vibrations  in  traveling  two  yards  from  their  origin 

must  spread  over  four  times  the  territory  which  they  cover 

in   the   first   yard   alone, 

nine     times     the     latter 

amount      in       travelling 

three       yards,       sixteen 

times  in   travelling   four 

yards,    and    so    on.      A 

person    at    C,    therefore 

(Fig.  24),   twice  as   far 

awav   as  a  person  at  B 

from      the      source      of 

sound  at .  /,  will  hear  the 

sound  onlv  one- fourth  as 

loud,   since   it   will   have 

si)read    over    four   times 


Fig.    24. 


the  space.  Stated  as  a  law,  then,  the  intensity  of  a  sound  in 
free  air  diminishes  as  the  square  of  the  distance  of  the 
listener  from  the  sounding  body.''' 


*The  difference  in  meaning  between  the  words  intensity  and  loud- 
ness sliould  l)e  noted.  Intensify  refers  to  the  energy  of  the  sound-vibra- 
tions— a  liliysical,  measuralile  quantity,  while  loudness  refers  to  the 
sensation  wiiich  the  Hstener  derives  from  the  auditory  nerve  after  this 
energy  has  been  communicated  to  it.  Intensity  and  loudness  are  there- 
fore related  as  cause  and  effect. 


souxn,  ,ixn  its  relation  to  music  39 

Actually,  however,  the  ettects  of  this  law  are  much  modified 
l)y  disturbing  elements.  Striking;  other  (jhjects,  s(jund>  are 
echoed  or  reinforced   (  pa^e  VJ ) ,  and,  when  the\- 

...  .'       Sound-waves 

originate   near  the   earth,  halt   ot    the   sphere   m    confined  to  a 

....         tube. 

which  the  sound-waves  tend  to  travel  is  e\'idently 
intercepted  h\'  the  ground.  'Jdie  more  the  territor\-  over  which 
the\'  are  allowed  to  spread  is  cfjiitracted  h\-  such  mean-,  the 
less  does  their  intensit\-  diminish  ;  and  when  they  are  ccjnlined 
t(j  a  tube,  thcv  ma\-  travel  for  long  distances  with  little  loss  of 
iniensit\-.  since  their  f(jrce  is  expended  onlv  slightly  h\-  friction 
along  the  walls  of  the  tube  and  by  the  amount  imparted  to 
these  walls.  The  French  physicist  Regnault  (1810-1S78),  in 
ex])erinients  conducted  through  the  Paris  sewers,  was  able  to 
hear  a  pistol  shot  distinctlv  for  a  distance  of  six  miles  when 
these  sewers  were  made  to  act  as  a  soimd-carr}"ing  tube. 
Speaking  tubes  furnish  an  illustration  of  one  of  the  practical 
uses  to  which  this  principle  has  been  put. 

Since  the  impact  of  the  air-particles  is  more  direct  as  the 
air  becomes  denser,  sound  is  then  carried  by  them  with  greater 
intensity ;    and.    converselv,    as    the    air   becomes    t^      •.        , 

•    '  •  -  Density  and 

rarefied,  its  intensity  is  lessened.  In  ver\-  ra'-ehed  '"tensity, 
regions,  stich  as  the  tops  of  high  mountains,  tn^  modihcation  of 
inten^it\'  is  so  decided  that  the  report  of  a  pistol  sounds  scarcely 
louder  than  that  of  a  hre-cracker  under  or(linar\-  ci'"cumstances. 
As  a  general  rule,  sounds  are  heard  with  more  distinctness 
at  night.  This  phenomenon  is  onlv  partly  accounted  for  by 
the   absence   of  confusing  noises   audible   in   the    „       .    ,     , 

'~  bounds   louder 

daytime,   and    is    ])robably   due   in    a    still    larger    ^'  night, 
measure  to  the   fact  that  the   air  is   in   a  more  homogeneous 
condition  at  night,  since  the  contlicting  heat  currents  induced 
b\-  the  sun   (page  20)   d()  not  then  exist. 

A\diy  the  intensity  of  a  sound  is  greater  in  the  direction  in 
which  the  wind  is  blowing  has  l)een  a  matter  of  considerable 
si)eculation.      I'erliai)s  the  most  i)lausi1)le  tlieorv    ^^        r    ■  ^ 

'  11^       Effect  of  wind 

i>   the   one   which   asserts   that,   as   the   air  ])l(nvn   "P°n  intensity, 
along  b\-  the  wind  is  retarded  b\-  friction  where  it  touches  tlie 


40 


SOUND.  AND  ITS  RELATION  TO  MUSIC 


earth,  the  sound-waves  are  bent  downward,  striking  the  listener 
with  greater  force.  On  the  other  side  of  the  sounding  b(jdy 
the  reverse  process  must  take  place,  since  the  lower  parts  of 
the  sound-waxes  are  less  antagonized  by  the  wind  than  the 
upper  ])arts,  and  the  waves  are  consequently  bent  upward,  thus 
becoming  weaker  near  the  earth.     In  Fig.  25  is  shown  the  action 


J  AC 

Fig.    25. 

of  the  wind,  which  blows  in  the  direction  of  the  arrow,  "hend- 
ing  down  the  sound-wa\es  from  the  vibrating  bod\"  C  in  the 
direction  of  /  and  inclining  them  upward  in  the  opixjsitc  direc- 
tion. Every  inter\-ening  oljject.  such  as  that  at  ./  tends  to 
increase  the  downward  slope  toward  /. 

Sdund-intensitv  is  also  much  affected  by  the  sympathetic 
vibrations  of  bodies  other  than  the  one  by  which  the  sound 
r>  J       is  produced.     This  ijhenomenon  is   discussed   in 

Kesonance  and  ^  ' 

intensity.  Chapter  \'I. 

Haxing  considered  the  intensity  of  single  sounrls.  let  us  now 

inquire  how  this  intensit\-  i>  affected  when  our  original  sound- 

waves  come  into  contact  with  those  arising  frrnu 

Nature    of    the  '.         , 

phenomena  of       other  Si  lurccs.     A  vcrv  Striking  example  ot  what 

interference.  ,  ..        "  '  .  - 

then  hap])ens  is  atlorded  b\'  tiie  action  ot  xvalcr- 
wa\-cs.  If  we  obser\e  the  ruffled  surface  of  a  lake,  we  ])ercci\c 
a  great  x'arietv  of  wa\'es.  the  smaller  su])erim])osed  (.n  the 
larger  in  the  form  of  ripples,  those  encountering  others  in 
their  jiatli  ])a-sing  over  tlieir  con\-olutions.  but  each  set  of 
zciTc'cs  f'rcscninii  its  idciififx  so  hnu/  as  its  oicray  lasts.      In 


SOUND,  AND  ITS  RELATION  TO  MUSIC 


41 


the  same  way  the  condensations  and  rarefactions  of  diflerent 
sound-waves  pass  through  those  of  other  waves  which  they 
encounter,  each  keeping  its  distinctive  character  throughout. 
Finally,  the  ear  has  a  wonderful  power  of  selecting  out  the 
sound-waves  which  have  periodic  vibrations,  and  the  mind, 
having  perceived  these  varieties  of  wave-frequencies,  proceeds 
to  assign  them  to  their  respective  causes  with  a  considerable 
degree  of  accuracy.  Hence,  hearing  a  multitude  of  sounds  at 
the  same  time,  the  hum  of  bees,  the  monotone  of  a  waterfall, 
the  rustle  of  the  leaves,  the  lowing  of  a  cow,  the  barking 
of  a  dog,  we  are  able  to  distinguish  between  all  of  them, 
and  to  form  judgments  as  to  the  character  of  their  origins. 
\'ery  loud  sounds  may,  of  course,  blot  out  very  soft  ones. 
But  even  in  the  case  of  great  disparity  in  intensity,  slight 
sounds  are  sometimes  perceptible,  on  account  of  their  dis- 
tinctive quality.  Thus  a  device  for  attracting  the  attention 
of  an  individual  in  the  midst  of  the  roar  of  mill  machinery  is 
to  produce  a  light  hissing  sound  between  the  -teeth.  The 
various  results  which  arise  from  the  meeting  of  different 
sound-waves  are  classed  under  the  head  of  the  phenomena  of 
interference. 

What  happens  now,  when  two  sounds  encounter  which  have 
the  same  vibration  numbers?  This  phenomenon  has  already 
been  noticed  in  connection  w^ith  sound-reflection 

.  Interference  of 

(page  20).     Let  us  assume  that  two  tunmg-forks    sounds  of  the 

,         .  ,  .      ,  ,.  ,  same   pitch. 

havmg  the  same  pitch  are  soundmg  at  a  short 

distance  from  one  another.     When  their  waves  meet,  one  of 


SOUND   AUCMtNTATlON    BY    CON 


RESONANCE     BOX 


42 


SOUND.  AND  ITS  RELATION  TO  MUSIC 


three  results  nuist  follow  :  the  condensations  from  the  one  fork 
may  be  added  to  those  from  the  other  and  the  rarefactions 
from  the  one  to  those  from  the  other,  in  which  case  tlie  sound 
is  greatly  augmented  (,  I'ig.  2()};  the  ctnidensations  from  one 
fork   may  be   imposed   ujxm    the   rarefactions    from   the   other 


RF-SONANCf.     BOX 


Fio.    27. 

(Fig.  27).  in  which  case  thc\-  neutralize  each  other,  and  the 
sound  is  nearh'  extinguished;  or.  as  is  most  frequent,  ihc 
wa\es  ma\-  meet  irregularl}-.  at  >ome  ])oint  between  those 
mentioned  in  the  llrst  two  cases,  when  the  intensit_\-  ma}  var\- 
either  one  wnv  or  another,  according  to  the  point  of  coniacl. 
This  effect  of  sound-interference  is  easil\-  demon>trate(l  be- 
holding a  >ounding  tuning-fork  jKirallel  to  one  ear.  wliile  the 
other  is  stopped  b\-  the  linger.     If  now  the  fork 

Interference  ,  ,  ,  '    -  ".  ...  .  , 

illustrated  by  a     !)e   >Iowlv  rotated,   tour  ])omts  will   occur  m   the 

tuning-fork.  "  ,        .  ,  ,  ,     . 

course   of   a   re\'olution   \\liere  the   sound   i>   ex- 
tinguished.    The  reason   for  these  silences  is  explained  when 
\\e     reflect     that     at     each     time 
the    ])r()ngs   of    the    fork    vibrate         ''•._ 
outward    the\-    not    onl\-    form    a  ';.,  "' 

condensation  b\-  their  impact.  Init 
also  ]ea\e  behind  a  corropond- 
ing  rarefaction,  in  the  >pace  be- 
tween them,  .'^imilarl}-.  on  their 
o])j)o-ite  swing,  thev  form  a 
condensation  in  the  central  s])ace 
while  a  rarefaction  is  left  m  tlie 
outside  air.      Two  sets  of   vilir:^-        "  Fi?.  28. 


/ 


A 


SOUND,  AND  ITS  RELATION   TO  MUSIC 


43 


lions  are  thus  i)roi)agaicd.  having  the  same  frequency  but 
f)p]x)site  phases;  and  the  waves  thus  generated  meet  along  the 
hues  extending  out  from  tlie  four  corners.  In  I'ig.  i(S  we 
are  su])i)Ose(l  to  look  down  u])on  the  end>  of  the  ])rong>  a  />. 
which  xihrate  outward  and  inward  as  ie])resented  In-  the 
arrows.  The  sound  will  be  strong  at  r  (/  c  and  /',  but  will 
be  <|uenche(l  along  the  lines  //  /;  ;'  k.  where  the  waves  neutralize 
each  other. 

Metal  plates,  known  as  Chladni's  plates  (page  61  ).  tend  to 
divide  up.  when  sounding,  into  seAcral  ecjual  sectors,  of  which 
those    adjacent    to    each    other    give    out    sound- 

.  .  .  Experiment 

waxes   ot    opposite   ])hases.   that    is.   one    is   pro-    with  metal 

.  plates. 

ducing    condensations    while    tlie    other    is    pro- 
ducing rarefactions,  and  z'icc  versa,   although   their   vibration 
numbers    are    the    same.       If    a    forked    tube    ('    /)    /:    i  Fig. 

-I ) .  cai)])ed  bv 
a  membrane  on 
which  ,^and  i^ 
s  t  r  e  w  n .  be 
]>lace(l  with  one 
of  its  prongs 
o\-er  each  oif  two 
alternate  sectors 
A  A  nr  B  /;.  the 
san<l  will  be  \i<  >- 
lentl}-  agitated, 
owing  to  syni];a- 
thelic  resonance 
( ])age  60  )  ;  but 
if  the  ])rongs  be 
|)laced  over  adjacent  sectors  A  B.  as  in  the  drawing,  the  sar.;! 
will  remain  undi>turbcd.  showing  that  the  two  sets  of  \ibra- 
tions  are  mutuall_\-  destructive. 

.\gain.  if  two  organ  pijjcs  of  e(|ual  dimen>ion-  be  fed  from 
the  same  \vind-che>t,  they  will  vibrate  in  o])po.-ite  ])hase.-.  and 


Fig.    29. 


44 


SOUND.  AND  ITS  RELATION  TO  MUSIC 


their  sounds,  instead  of  being  reinforced,  will  be  nearly  ex- 
tinguished.    Organ  builders  are  obliged  to  guard 

Experiment  ...  .  ... 

with  organ  agaiust    this    contingcnc}',    m    constructing    their 

pipes. 

instruments. 
Having  discussed  the  results  which  occur  when  two  equal 
sounds  having  the  same  vibration  number  come  into  conflict, 
let  us   now   consider   what  happens   when   these 

Interference  .  _.  ...  , 

of  sounds  of        two    souuds    havc    different    vibration    numbers. 

different  pitches.     ,,  ,  .        .,  .  _^  ,      „ 

Suppose  that  two  sets  of  vibrations  V  and  h 
are  travelling  in  the  same  direction,  starting  in  opposite  phases, 
so  that  the  first  vibration  of  /)  is  neutralized  by  that  of  E. 
If,  now,  E  be  travelling  faster  than  D,  it  will  gradually  gain 
upon  D  until  a  condensation  pulse  of  E  corresponds  with  one 
of  D.  Still  gaining  on  D,  E  now  i)asses  along  until  the  vibra- 
tions are  again  in  opposite  phases,  and  the  sound  becomes 
again  inaudible.  At  this  point  D  will  have  made  an  entire 
vibration  more  than  E,  and  the  sound  will  ha\-e  grown  from 


Fig.    30. 

zero  to  a  climax  and  then  ha\e  diminished  to  zero  again. 
Fig.  30  illustrates  this  process.  1  lere  D  is  represented  by  the 
dotted  line,  and  E  bv  the  C(Minected  line.  The  opposing  phases 
are  at  A  and  B.  and  the  climax  of  intensity  at  (  . 

Such  an  increase  and  decrease  of  sound  has  Ijeen  given  the 

name  of  a  beat;  and  it  is  evident  that  one  of  these  beats  must 

occur  whenever  one  set  of  sound-waves  gains 

Beats    and 

their  frequency,  over  another  by  a  single  vibration.  Thus  if  a 
sound  vibrating  100  times  ])cr  second  travels  with  one  which 
vibrates  101  times  in  the  same  interval,  one  l)eat  per  second 
will    result  ;   if   the   first   sound    vibrates    100   times    while    the 


SOUND.  AND  ITS  RELATION  TO  MUSIC 


45 


second  vibrates  102  times,  there  will  he  two  beats;  and  so  on. 
(liven  the  vibration  number  of  one  sound,  therefore,  it  is  easy 
to  determine  that  of  another  wdiich  vibrates  nearly  in  unison 
with  it,  simply  by  counting  the  number  of  beats  per  second 
which  they  cause  wdien  sounding  together,  and  adding  or  sub- 
tracting these  from  the  vibration  number  of  the  first  sound, 
according  as  the  second  sound  is  sharper  or  flatter.  It  is  on 
this  ])rinciple  that  the  vibration  ntmibers  of  sounds  are  reckoned 
from  the  tonometer  (page  28).  Tuners  of  instruments,  also, 
gauge  the  accuracy  of  their  work  by  noting  the  beats.  A 
piano  tuner,  for  instance,  adjusts  a  string  so  that  no  beats 
occur  between  it  and  the  tuning-fork  with  which  it  should  be 
in  unison.  As  there  are  generally  three  strings  to  each  tone, 
the  other  two  strings  are  then  stretched  until  they  make  no 
beats  with  the  initial  string,  when  their  unison  with  it  must 
be  perfect. 

As  the  difference  betw^een  the  vibration  numbers  of  two 
sounds  increases,  the  beats  quicken  until  they  blend  together, 
The  result  of  J"^^  ^^  ^^^^  spokes  bccome  iifdistinguishable  when 
quick  beats.  ^  wheel  revolves  quickly.  The  effect  of  unrest 
remains  up  to  a  certain  point,  however,  voicing  itself  in  w'hat 
is  commonly  called  a  discord  l)etween  the  two  tones  (page  98). 


Fig.   31. 


46 


M)uxp.  .i.\/>  rr.\  h'li/.ATiox  to  music 


l.issajous   (1<S22-1880)    dcxiscd  an  a])i)aralus  l)y   which  the 

combined    resuUs   of   the   \-ihrations   of    the   two   tuning-forks 

could   he   thrown   upon   a   screen.      An   improved 

Lissajous'  ...  .  ,,.  ^^  ,,  - 

apparatus    for  fonU      of      tluS      rs      sllOWU      lU      1' Ig.      >")  1  .         ()1      tWo 

recording  beats.  .  .  ,  .       /  ,. 

tuiung-lorks  ./  and  B ,  one  is  kept  soundmg  1)\ 
means  of  an  electric  current,  while  the  number  of  vibrations  of 
the  other  is  regulated  by  a  sliding  weight  on  one  of  its  prongs. 
By  means  of  a  style  attached  to  the  end  of  each  fork,  the 
combined    \ibrations    are    recorded    on    a    snioked-'j!-' -s    ijlate, 


Fig.    32. 

and  thrown  upon  a  screen  by  the  lantern  at  the  loj)  of  the 
ap])aratus.  Dr.  Koenig,  using  a  similar  device,  obtained  the 
results  shown   in    I'ig.   32. 


SOUND,  .'IMP  ITS  RliLATlON  TO  MUSIC 


47 


Beats  occasioned 
by   defects   in 
instruments. 


.Man\-  oilier  condilit ms  I)esi(lc  tliosc  descriljcd  nvdx  ,^ive  rise 
to  heats.  Defects  in  a  musical  instrument,  causing-  its  parts 
to  vibrate  out  of  unison,  mav  ])ro(luce  tlieiu  :  thus 
ue  often  hear  l)eats  in  the  tone  of  a  hell,  owiui^" 
to  the  fact  thai  it  divides  into  .'■■•^■nienls  when 
soundiui^'  and  that  these  segnienls  have  imi)erfections  in  con- 
struction which  puts  them  slit^htl\-  out  of  tune  with  each  other. 

I'lcats  are  ])ro(luce(l  not  onl\-  l)y  the  fundamental  tones,  hut 
also  1)\-  the  iip/^cr  /^artials  or  (n'crfoiics  which  accompany  them 
in  most  musical   sounds    ( i)aije  51),  when   these    r,    ,    . 

1      -^  Beats   from 

overtones    (litter    from    one    another    slii^htlv    in    overtones, 
'pitch.      Accordini^l}-,    the    interference    of    two    complex    tones 
may  invoh'e  a  \'ariet}'  of  beats  of  dilterent  degrees  of  loudness 
and  (.)f  rapidit}'. 

When  we  hear  two  loud  tones  of  ditTerent  ])itches  sounding 
together,  we  are  sometimes  ccjnscious  of  the  presence  of  a  third 
lone,  lower  in  pitch  than  either  of   them.      Tar-    „      ,^ 

i  Resultant 

lini  (  16')2-177(}).  the  noted  violinist,  is  said  to  t°""- 
have  first  drawn  attention  to  the  existence  of  such  t(mes,  and 
in  his  honor  the\-  were  formerly  called  l\vt'uu's  fours,  although 
lliey  arc  now  generallv  known  as  resultant  tones.  The  follow- 
ing table  shows  in  black  notes  the  resullant  tones  j)r(Mluced  b\- 
the  chief  intervals  included  within  the  diatonic  scale,  repre- 
sented by  white  notes  on  the  upi)er  staff   ( h'ig.  3vV)  : — 


P(t4'I'       M«j  .'J"!      .M, „..■;»'      Maj  6'h       Min6'J' 


Fig.    33. 

Perhaps  the  reed  organ  is  the  best  available  instrument  with 
which  to  experiment  with  resultaiu  tones.  They  are  not  alwa\-s 
„  ,  easiK'   i)erceptible  ;  but  if  the  tone  of  the   same 

How   to   hear  -       '  ' 

these  tones.  piteli  as  the  resultaut  tone  be  ])reviously  sounded, 

the  latter  can  be  more  readil\-  detected  when  its  generators  are 
nlaved. 


48  SOUND,  AND  ITS  KELATION  TO  MUSIC 

What  causes  these  tones  is  still  a  matter  of  controversy. 
Since  the  vibration  number  of  a  resultant  tone  was  found  to 
„  ,   ,   „  ,  be  equal  to  the  difference  between  the  vibration 

rlelmnoltz  s  ^ 

res^uitant*^  uumbcrs  of  the  generating  tones,  and  is  there- 

'°"^^-  fore  of  the  same  frequency  as  the  beats  which 

they  produce,  it  was  at  first  supposed  that  the  resultant  tones 
were  caused  l)y  these  beats.  Helmholtz,  however,  discredited 
this  theory  on  the  ground  that  the  resultant  tones  and  the  beats 
were  sometimes  heard  simultaneously ;  and  he  therefore  ad- 
vanced the  theory  that  when  the  amplitudes  of  the  vibrations 
of  two  sounds  are  very  great  these  set  in  motion  other  sound- 
waves, different  from  either  of  the  original  ones.  From 'this 
theory  he  also  deduced  the  existence  of  what  he  called  sum- 
mational tones,  whose  vibration  numbers  are  equal  to  the  sum 
of  those  of  their  generators.  What  we  have  described  as 
resultant  tones  he  distinguished  as  differential  tones. 

Dr.  Koenig,  however,  as  the  result  of  manv  intricate  experi- 
ments, reverted  to  the  former  theory,  renaming  resultant  tones 
„     „      .  ,  beat-tones.     In  support  of  this  theorv  he  not  onlv 

Dr.    Koenig  s  ^  ' 

theory.  ])roved  that  a  tone  and  the  rattle  of  the  vibrations 

which  produces  it  can  sometimes  be  heard  simultaneously,  but 
also  showed  that  many  of  the  phenomena  connected  with  result- 
ant tones  arc  explainable  only  on  the  hypothesis  that  they  are 
caused  bv  the  beats.  Tt  is  also  a  matter  of  dispute  as  to 
whether  these  tones  reallv  exist  in  the  outside  air  or  are  formed 
within  the  cavity  of  the  ear  itself,  Helmholtz  advocating  the 
former  view  and  Dr.  Koenig  the  latter. 


SOUND,  AND  ITS  RELATION  TO  MUSIC  49 

SUMMARY 

The  loudness  of  a  sound  is  proportional  to  the  square  of  the 
amplitude  of  its  vibrations.  X'ariation  in  this  amplitude  does 
not  affect  the  pitch. 

In  free  air,  sound-intensity  is  inversely  proportional  to  the 
square  of  the  distance  of  the  listener  from  the  sounding  body. 
When  sound  is  restricted  to  the  boundaries  of  a  tube,  however, 
it  proceeds  with  little  lessening  of  intensity. 

Sounds  are  louder  in  dense  than  in  rarefied  media,  and  are 
also  generally  louder  at  night.  They  are  intensified  in  the 
direction  in  which  wind  is  blowing,  and  softened  in  the  con- 
trary direction. 

The  results  which  follow  when  two  sets  of  sound-waves 
meet  are  called  the  phenomena  of  interference. 

When  two  sounds  of  unison  pitch  and  equal  intensity  meet, 
the  individual  intensity  of  each  may  be  augmented  up  to  twice 
what  it  was  at  first,  or  it  may  be  reduced  even  to  complete 
extinction. 

If  the  two  sounds  are  not  in  unison,  undulations  in  intensity 
known  as  beats  occur,  of  which  the  number  per  second  equals 
the  dift'erence  between  the  vibration  numbers  of  the  sounds. 
X'arious  conditions  give  rise  to  beats.  They  are  useful  for 
determining  exact  vibration  numbers. 

Two  loud  sounds  are  sometimes  accompanied  by  a  resultant 
tone,  the  nature  of  which  is  disputed  by  physicists. 

REFERENCE  LIST. 

HeUnhohz.  Chapters  2.  4.  7,  11. 

Tyndall.  Chapters  1,  8,  9. 

Zahm.  Chapters  2,  7. 

Harris,  Chapters  6,  12.  13. 

Catchpoo!.  Chapters  4,  8. 

Taylor,  Chapter  2. 

Poyntiuy  and  TJioiiipson,  Chapters  1,  10. 

Stone,  Chapters  3,  5. 

Broadhousc.  Chapters  5,  12,  14. 

Blascrna.  Chapters  2,  5. 


50  SOUXD.  ,1X!)  ITS  RELATIOX   TO  MUSIC 

Meyer.  Chapters  8.  13,  14. 
Bar)ies,  Chapters  9.  12. 
IJartotJ.  Chapters  1,  7, 
Pole,  Chapter  3. 


CKAI'TER  V 

OiJAi.nv 

TuF.  third  property  of  sound,  that  of  quality,  enahles  us  to 
(Hstinguish  helween  sounds  c\en  if  they  Ije  of  the  same  pitch 
and  eciual  loudness.     In  Hstenin"'  to  an  orcliestra,    „,        ,    .  .. 

1  f^  '     Characteristics 

for  instance,  we  recognize  without  (ht^cuUy  the  °^  quality, 
tones  ])ro(hiced  b\'  the  viohns,  the  tiutes.  the  oboes  and  the 
lruni])ets  h\-  the  characteristic  ([uahty  of  each.  W  e  are  alstj  able 
\o  (h'aw  chstinctions  between  two  instruments  of  the  same 
species,  sax  iny  of  two  \iohns  that  the  one  is  smor)th  and 
pleasant  in  tone  while  the  other  is  rough  and  disagreeable. 
Again,  under  the  lingers  of  an  artist  a  violin  niav  give  out 
niehnlious  and  thrilling  tones,  while  the  same  instrument  con- 
stantl}-  offends  our  ears  when  handled  b\-  an  unskilled  amateur. 
There  are  thus  unlinuted  gradations  in  tone-character:  grada- 
tions which  ;ire  so  analogs 'Us  to  shades  of  color  that  they  arc 
often  spoken  of  bv  musicians  as  -zwictics  of  f<'iir-color. 

.*^cientists  iuv  a  long  time  found  luuch  difficidt}'  in  exi)laining 
the  phenomena  of  soun(l-(|uality.  Joseph  .^aux'cur  (  1653- 
171o).  the  inventor  of  the  wcn'd  "acoustics,"  and 

1       1  ,  1  1-  Tlieories  as  to 

se\eral  others  advanced  the  tlieory  that  quaht\-  the  nature  of 
is  i)roduced  b\-  the  combination  of  secondarx^ 
sounds  with  the  chief  tone;  but  no  adecjuate  de\'elo])ment  of 
this  idea  was  j^resented  until  1  lelmholtz  brought  out  his 
authoritative  work,  which  contained  a  full  and  conclusive  study 
of  the  subject.  In  this  he  clearly  proved  that  almost  every 
musical  tone  consists  not  only  of  a  principal  tone,  but  also 
of  a  number  of  subordinate  tones  of  lesser  intensity. 

To  these  secondar\-  tones  several  names  such  as  oz'crtoiics 
and  haiimviics  have  been  given.  The  latter  term  was  applied 
bv    Sau\eur    (mi    the    theorv    that    the    numerical    „      ,  u    . 

Use  of  the  term 

relations  which  their  vibrations  bore  to  those  of    "partiais." 
the  principal  tone  could  alwa\  s  be  expressed  by  whole  numbers 

51 


52  SOUND,  AXD  ITS  RELATION  TO  MUSIC 

in  the  series  2,  3,  4  and  so  on.  It  has  since  been  discovered, 
however,  that  in  many  instances,  notably  in  connection  with 
rods,  bells  and  plates,  these  relations  are  much  more  complex 
than  was  at  first  suspected.  A  more  comprehensive  nomencla- 
ture, therefore,  designates  all  the  tones  which  combine  to 
produce  the  total  effect  from  a  single  sounding  body  partials. 
The  lowest  of  these,  which  is  generally  also  the  most  promi- 
nent, is  the  fundamental,  while  the  others  are  upper  partials. 
Those  whose  relations  to  the  fundamental  can  be  expressed  in 
simple  whole  numbers  are  called  harmonic  partials,  while  the 
others  are  called   inharmonic  partials* 

Ilelmholtz   demonstrated  the  important  law  that  the   char- 
acter of  an  individual  tone  is  determined  by  the  number  and 
position  of  the  upper  partials  and  their  relative 

Laws  governing 

the  quality  of  a    intensities.     Dr.  Koenig  afterward  showed  that 

tone. 

quality  was  also  affected  by  the  relative  po>itions 
of  the  condensations  and  rarefactions  of  the  upper  partials.  or 
their  dift'erence  in  phase.  It  can  readily  be  seen,  therefore, 
that,  since  a  multitude  of  combinations  of  the  upper  partials 
may  occur  with  ever\-  varietv  of  intensitv  and  with  still  other 
modifications  through  variations  in  phase,  there  is  practically 
no  limit  to  the  number  of  possible  gradations  in  tone-quality. 

A  clever  device  called  a  reso- 
nator (  Fig.  34 )  for  detecting 
and  studying  upper  partials  was 
invented  by  Ilelmholtz.  This 
u  ,    -   ,.  .  is  in  the  form  of  a 

Helmholtz  s 

resonators.  lloHoW      globc      bcSt 

made  of  thin  brass,  having  a 
small  aperture  h  on  one  side  with 
a  pn  ijection  which  can  be  inserted         ^'s-  34.  ndmhoitz--  Resonator 


T;u-  reader  should  be  careful  not  to  confuse  the  terms  partials 
and  upper  partials.  the  former  name  includiny  both  the  u[)j)er  partials 
and  tlie  fundamental.  Thus  the  fundamental  is  the  first  !)artial,  the 
first  upper  partial  is  the  second  partial,  the  second  upper  partial 
is  the  third  partial,  and  so  on. 


SOUND,  AND  ITS  RELATION  TO  MUSIC  53 

in  the  ear,  while  a  larger  opening  a  in  the  opposite  side  admits 
the  sound-waves  from  the  outer  air.  In  accordance  with  the 
I^rinciples  of  resonance  explained  in  the  next  chapter,  this  in- 
strument has  the  power  of  selecting  out  a  single  tone  to  which 
it  is  tuned  and  of  reinforcing  this  tone  so  that  it  strikes  the  ear 
with  greatly  increased  intensity.  By  constructing  a  number  of 
these  resonators  tuned  respectively  to  the  various  degrees  of 
the  scale,  lielmholtz  was  able  to  listen  for  the  appearance  of 
upper  partials  in  a  given  sound  and  to  determine  the  pitch  and 
intensity  of  anv  one  of  these  by  its  agreement  with  the  pitch 
of  its  sympathetic  resonator. 

In  this  manner  it  was  discovered  that  only  in  a  few  instances, 
including  mainly  the  tones  prodticed  by  some  tuning-forks  and 
stopped  organ  pipes,  was  there  an  approach  to    ^^^^^^  ^^  ^ 
an  absolutelv  simple  tone.     Moreover  such  pure    tone  produced 

t^  '  by  aaaing 

tones,  while  pleasant  to  hear,  quickly  become  un-  paft'a's. 
interesting.  With  the  addition  of  simple  harmonic  partials, 
character  and  vitality  is  imparted  to  a  tone ;  while  an  ad- 
mixture of  remote  overtones  results  in  more  pungency  and 
incisiveness,  frequently  accompanied  by  discordant  elements. 
Unfortunately,  the  range  of  tone  recognizable  by  the  resonators 
does  not  extend  to  sounds  very  acute  in  pitch,  so  that  it  is 
difficult  to  investigate  the  character  of  the  highest  upper 
partials. 

While,  therefore,  it  is  comparativelv  easy  to  analyze  the 
simple  harmonic  partials  of  a  given  tone,  it  is  a  more  difficult 
task  to  reconstruct  this  tone  if  it  contains  partials    „      ,  , 

t  How  far  vowel 

bcvond  the  reach  of  resonators.     This   fact  has    rounds  can  be 

reproduced 

made  the  problem  of  reproducing  the  varieties  of  artificially, 
vowel  sounds  hard  to  solve.  lielmholtz.  Koenig  and  others, 
recognizing  that  the  peculiar  characteristics  of  spoken  vowels 
are  caused  by  certain  combinations  of  upper  partials,  have 
made  many  attempts  to  mimic  these  sounds  l)y  artificial  ineans. 
I'v  sounding  together  tuning-forks  of  ])itches  and  strengths 
corresponding  to  the  ascertained  values  of  the  partials,  an 
approach  was  made  in  some  cases  to  the  original  sounds ;  but 


54 


SOIWD.  ,l.\D  ITS  RliLATIOK  TO  MUSIC 


owing  to  the  impossibility  of  providing"  for  many  inharmonic 
])artials  outside  the  scope  of  the  resonators,  some  of  these 
experiments  proved  less  successful,     h'ig.  3,^  depicts  an  elabo- 


Fig.    35. 

rate  instrument  made  ])\-  Koenig,  consisting  of  ten  reinforced 
tuning-forks  which  can  be  ])ut  into  \ibration  1)\-  means  of  an 
electric  current.  The  keyboard  in  front  allows  the  operator 
to  throw  (jn  an\'  combination  of  the^e  forks  which  he  wishes, 
regulating  al>o  at  will  their  relati\e  intensities.  \\x  means  of 
this  instrument  the  \'o\vels  //  (as  in  boot),  o  (as  in  no),  and 
(/  (as  in  ah]  have  been  reproduced  with  considerable  lidclit}  : 
but  onlv  a  slight  suggestion  can  be  gi\cn  oi  those  \'owel  sounds 
which  contain  complex  and  actUr  ]iartials,  such  as  the  sounds 
of  e  and  /. 

I'or    the    investigation    of    the    h.armonic    partials    the    liest 

medimu  is  the  sfrctchod  striiui.  some  of  the  laws  of  which  we 

ha\'e    alrcadx'    .-studied    in    L"ha])ter    lib       I.ct    us 

Production    of  .  .         '  ^  ^ 

partials  from         agaui  rclcr  to  the  sonometer  sliown  on  ])agt'  .").■>. 

strings. 

Ilavimr     tuned     one     of     the     strings     to     bass 


SOUND.  AND  ITS  RliL.  IT/ON  TO  MUSIC  55 

C  ^==^  ,  let  us  touch  a  feather  to  the  middle  of  the  string 

and  pluck  the  string  half  \va\-  between  the  point  touched  and 
one   of   the  ends.      We   now   clearlv   hear  the   second   partial. 

which   is  the  note  r  ;3'^ -li^^     .  just  an  octave  above  the  tirst 

partial  or  fundamental.  This  new  tone  is  produced  by  each  of 
the  two  ecjual  i)arts  into  which  the  string  is  di\ided.  and  each 
of  which,  according  to  the  laws  of  stretched  strings  (page  33), 
must  be  \ibrating  twice  as  fast  as  the  whole  string.  Where 
the  feather  tt)uches  the  string  there  is  scarcely  any  motion  at 
all.     This  point  is  named  a  node.     At  the  middle 

11      1         1    •    1        Nodes  and 

ot  the  'c'Ciifral  sc(j)nciits,  as  thev  are  called,  which   ventral  seg- 

.   ,  '   .  ,  .      ,  '  ,  .  ments. 

occur  on  either  side  ot  the  node,  are  the  points 
of  greatest  motion.     If  the  feather  be  removed  from  the  string 
the   latter   will    continue   to   vibrate   in   halves   as   long   as   its 
momentum  lasts. 

Likewise,  damping  the  string  at  one-third  of  its  length  will 
divide  it  into  three  \entral  segments  separated  bv  two  nodes; 
and    the    third    partial    thus    gi\en    out    will    be    ^,,  ,.  , 

'  "^  Other  partials 

an    ocia\e    and    a    fifth    above    the    fundamental    °^  strings. 

y^^~"^'^  .      Again,   the    fourth   i)artial.   made   by   dividing  the 

string    into    ([uarters.    will    Ije    one    octa\e    abo^•e    the    sec()nd 

^rE^   ,  while  the  tifth  partial,  produced  by  a  division  into 

fifths,    gives    the    note    a    major    third    abo\e    its    predecessor 

^  .      It    should   be  observed   that   the   two  ends   of   the 

string  in  each  case  form  two  (,)ther  nodes,  in  addition  to  those 
enumerated. 

An  interesting  ex])erinient  is  perfcjrmed  bv  i)lacing  a  number 


56 


SOUND,  AND  ITS  RELATION  TO  MUSIC 


of  small  bent  pieces  of  paper  or  "riders"  upon  the  string  before 
„       .      ,  it  is  sounded,  red  ones  where  the  nodes  should 

Experiment  ' 

with  "riders."  appear  and  blue  ones  on  the  ventral  segments. 
When  the  string  is  put  into  vibration  the  blue  riders  will 
instantly  be  unhorsed,  while  the  red  ones  will  retain  their 
position.     This  effect  is  shown  in  Fig.  36. 


Fig.    36. 

Continuing  still  further  to  divide  up  the  string  into  integral 

parts,  we  may  form  any  number  of  segments  and  their  accom- 

panving  nodes.     For  j)ractical  uses,  however,  only 

The  "harmonic  ."'^.,,  .  .,  ,,  ., 

series"   of  a  icw  01  the  harmouic  partials  need  be  consid- 

strinsTSi 

ered.  The  brst  sixteen  of  these  for  the  note  C 
are  shown  in  b^ig.  37.  The  vibration  numbers  indicated  beneath 
are  calculated  on  the  basis  of  the  scientific  jntcb.  which  is  somc- 


64     128    192 


.      6       7       S       9       10     11     12     13     li     15     1» 

250   320    3H4    448    512    576    640    704   768   872    8U6  960  1024 


The  Ilarnionic  Series 


what  lower  than  the  international.  Note  also  that  the  partials 
indicated  by  black  notes  are  slightly  out  of  tune  with  the  cor- 
responding tones  in  our  scale. 

Let  us  now   inquire  what  are   the  motions   which   a   string 


SOUND,  AXI)  ITS  RliL.-lTlUX  TO  MUSIC 


Fig.    38. 


makes  wlien  tlie  presence  of  several  upper  partials  causes  it 
to  vibrate  in  a  ntunl)er  of  dilTerent  directions  at 

Complex 

the  same  time.     I-'i',''  38  shows  some  of  the  simpler    motions  of 

■^  .  strings. 

of   these  motions.      If   the   strmg-  ./   M   B   gave 
out  onlv  its  fundamental,  it  would  assume  the  uniform  curve 
./    C  B.     When,  however,   the   string,  besides  vibrating  as  a 

whole,  also  di\-idcs  up 
into  segments,  these 
must  adapt  themselves 
to  the  fundamental  vi- 
bration, appearing  as 
alternate  elevations  and 
depressions  along  the 
length  of  the  string. 
Thus  when  .  /'  M'  B'  vibrates  in  its  entirety  and  also  in  halves, 
the  segment  on  one  side  moves  outward  when  that  on  the  other 
>ide  moves  inward,  and  vice  versa,  so  that  positions  like 
A'  C  B'  are  assumed.  Again,  . /"  M"  B" ,  sounding  its  funda- 
mental plus  the  second  upper  partial,  takes  positions  corre- 
sponding to  the  curve  A"  D  D'  B" .  As  other  overtones  are 
added,  the  motions  increase  in  complexity,  each  partial,  how- 
ever, preserving  its  individuality.  This  complexity  is,  of 
course,  transferred  to  the  resulting  sound-waves,  in  which  the 
various  condensations  and  rarefactions  are  correspondingly 
superimposed  upon  each  other. 

Given  upper  partials,  however,  can  exist  only  when  condi- 
tions are  favorable  for  the  formation  of  their  nodes  and 
ventral   segments.      If,   for  instance,  a   string  be    ^     ... 

'^  f^  Conditions 

ijlucked  at  its  centre,  there  must  be  a  maximum    ""'^^''  which 

1  given  partials 

of  viljration  at  this  point  and  hence  it  cannot  ^^^  occur, 
become  a  node.  C'onsequentlv  all  the  partials.  such  as  the 
second,  fourth  and  eighth,  which  have  a  node  at  the  centre, 
are  ai)sent.  Again,  sounding  a  string  at  a  point  where  the 
node  of  a  discordant  ]iartial  would  l)e  formed,  the  tone  becomes 
inorL'  agreeable  b\-  the  eliminatitai  of  such  partial.  Hence  the 
skilled  violinist  draws  his  bow  at  the  most  favorable  division 


58 


MJLW'D,  .1X1)  ITS  REL.-ITIOX  TO  Mi'SIC 


of  the  strings,  and  tlie  piano  maker  care  full  \-  disposes  his 
liainnier   strokes   to   ])ro(luce   the   hest   tonal   (|ualit}-. 

The  \'il)rations  of  Ijodies  other  than  >tring"s  are  go\-erne(l  hy 
more  or  less  divergent  conditions.  Turning  to  the  suhject  of 
^       ,      r      ,      sciiiiiliiKi  rihis.  let   us   first   examine  the  m(*tions 

Partials  of  rods 

fixed  at  one  end.  , , ,-  ^  ,-, ,^1  fixed  at  ( mc  cud  and  free  at  the  other. 
In  I'ig.  3''  a  rorl  thus  located  oscillates  as  a  whole  hetween 
the  ])ositions  indicated  h_\'  the  dotted  lines  p  o  and  p'  o.    With 


Fit;.    40. 


the  ad\ent  of  the  second  jiarlial  the  fixed  end  niu:-t  fi)rni  a 
node,  hnl  the  free  end,  unrestricted  in  its  nioiiiin.  heconie-  the 
centre  of  a  \entral  segment.  T\'v  other  node  niu<l  tliereii  ire  ( ic- 
cur  at  a  di-iance  of  a  h.alf  segment,  or  one-thirrl  of  the  length 
of   the  \'il)ralim''  portion   '•'   the    rod,   helow   the    free   end,   the 


SOi'Xn.  .-I.\7)  ITS  RI-I.,lTIO\'  TO  Ml'SlC  5') 

remainder  of  the  r(xl  f(jrniing  a  whole  segment  ( l"iy.  4;)i. 
Likewise  wlien  the  third  partial  ari>e'-,  the  rod  form>  two  and 
one-half  ventral  segments,  with  the  lir>t  node  located  at  one- 
llfth  of  the  length  from  the  free  vud.  while  each  of  the  entire 
segments  ()ccn])ies  two  of  the  remaining  four-tifths  (  I'ig.  41  ). 
Succeeding  partials  would  continue  to  di\ide  the  rod  according 
to  the  odd  numl)ers.  7,  [).  11.  Cvc. 

These  upper  ])artials  ri-e  very  rapidly  in  pitch,  and  are 
inharmothc  in  character.  Thus  the  I'lrst  up])er  partial  has 
ahout  6'. 4  as  manv  \ibrations  as  the  fundamental, 

1    M         1  1     "       1  -     /  w  Relations     of 

while  the  next  has  l/'j  as  man\'.     We  can  verv    these  partiais  as 

to  pitch. 

readiK-  hear  the  high  o\'ertones  which  ring  out 

as  we  strike  a  tuning-fork,  but  which  afterward  vanish,  leaving 

the  fundamental. 

A  tuning-f(jrk  is  subject  in  each  of  its  branches  practically 
to  the  -ame  laws  as  are  rods  fixerl  at  one  end.  Wdien  gi\ing 
oui    its   fundamental   it   \ibrates   with   a   node   at    ^    ,•  ,      , 

Partials   of 

the  lower  extremity  of  each  Ijranch,  which  corre-    tunii^g-forks. 
>l)onds  to  the  hxed  end  of  the  rod.     The  three  segments  thus 
formed  \ibrate  in  unis(jn  with  one  another.     Two  other  nijdes 


6i 


i7i 


are  formed  ujion  the  appearance  of  the  -econd  n].per  ])artial, 
and  still  two  more  with  the  third,  these  ui)])er  i)artial>  bearing 


60 


SOrXD.  AX/J  ITS  RliLATIOX  TO  MUSIC 


the  same  relations  of  6/4  and  17' j  viljrations  resi)ectivelv  to 
their  fundamental  as  did  the  rods  before  discussed  (  see  l""ig. 
42 j.  It  shoukl  be  nuied,  however,  that  the  viljrati(jn  number> 
^■arv  somewliat  in  the  case  of  forks  of  ditterent  .-hapes  and 
materials. 

Rr)ds  with  biith  end<  free,  emploxed  in  instruments  like  the 

.vxhif'lioiir  and  inctalloplioiic.  were  investigated  with  great  care 

b\-   L'hladni    (  175()-18i7  ),   who  has   received   the 

Vibrations   of  "         ,,       ■  -   .    -       i  -  i  ■         ■■     ti 

rods  free  at  both   a])])enatii)n  ot     tather  ot  modern  acoustic>.      the 

ends.  .  .  .  1111 

primarx'  motions  ot  such  a  rod  are  seen  by  liold- 
ing  a  -i\-f<M)t  flexible  stick  about  a  foot  from  each  end.  When 
the  stick  i>  -liakcn  it  oscillates  between  the  positiijns  shown  in 
./.  big.  43.  the  points  at 

which  it  IS  held  tornung        1      ;  ;       1       I    "  ■  I 

nodes.  Held  nearer  the 
ends,  it  \'il)rates  a> 
tinder      B.      with      three 

nodes.       As    its     funda- 

,    1  1  •    ,  Fig.   43. 

mental,      which      occurs 

wdien  the  two  n(jdes  abnie  arc  iM'escnt,  a  free  rod  gi\'es  (jut  a 
tone  ')'4  times  as  acute  as  the  fundamental  of  a  similar  rod 
tixed  at  <.ine  end.  or  a  tone  corre>ponding  t(j  the  tirst  upper 
])ailial  of  the  latter.  The  sttcceeding  ])artials  rise  rapidlv  in 
l»itch,  bearing  al)ijut  the  sante  relations  to  their  fundamental 
a-  those  in  connection  with  rods  hxed  at  one  end. 

Longitudinal  ^■ibrations  mav  be  ])rriduced  in  a  rod  b_\-  clamp- 
ing it  in  the  middle  and  rubbing  one  sectitjn  lengthwise.      If 

m   ivor\-   l)all 

te    sus])enrled 

lyainst  o  n  e 
end  of  the  rod,  a-  in  bdg. 
44,  it  will  be  re])elled  vig- 
orou-l_\-.  Savart,  indeed, 
founrl  that  it  wa-  i^o-.- 
sibie.  b\-  thur-  rubbing  a 
Lda'is   tube    with   a   wetted    cloth,    t 


Partials 

produced  when 
rods    vibrate 
longitudinally. 


Fig.    44. 

diatter   one   end   of    it   bv 


SOl^ND.  .IX!)  ITS  RliL.lTlOX  TO  MUSIC 


61 


the   force  of  its  own  molecular  motion.      l^Vee  rods  \ibratini,^ 
lonoitiulinallv  may  be  divided  into  2,  3,  4,  5  .segments,  and  so 

on,  the  \iljraticjns  of  which  fcjrm 
harmonic  parlials  like  those  of 
strings.  W  hen  the>e  rods  are  fixed 
at  one  end,  the  tones  which  they 
dex'elop  are  in  the  order  of  tlie 
uneven  harmonic  partials.  1,  3,  5 
and  so  forth.  A  curitais  instrument 
devised  by  Marloxe  (  179.S-1S74)  is 
furnished  with  rods  of  wo(k1  or 
glass  which  arc  pla}'C(l  u])()n  by 
rubbing  lengthwise  with  rosined 
fingers    (  h^ig.  45  ) . 

Chladni  conducted  a  series  of 
interesting  experiments  while  study- 
ing   the    motions     of 

*         .  Chladni's 

sounding         glass         or     experiments 
with    plates. 

metal    plates.       Some 

of   his   results   ma\'   be   appreciated 

bv  emplo\"ing  a   square   ])latc  tixed 

to  a  support  in  the  middle.     If  fine 

sand     be     strewn     upon     this 

l)late   and    the   plate   lie   made 

to  sound  b)'  drawing  a  violin 

bow   against   one   edge,   as   in 

Vig.  46,  the  sand  will  be  vio- 

lentlv  agitated.     Tress  a  finger 

at  the  middle  of  -. >ne  side  and 

the  sand  will  colled  along  the 

four    intersecting    nodes    thus 

generated.     Tn  h^ig.  47,  which 

shows   the   result   of   this   ex- 

])erimenl.  the  ])lus  and  minus 

signs    indicate   that    the    aher- 

Fi„.  46.  nate  segments  are  vil)rating  in 


Fig.    45. 


62 


SOUND,  .INI)  ITS  RELATION  TO  MUSIC 


opi^osite  phases;  that  is,  that  when  one  segment  vil)rates  out- 
ward, tlie  (jnes  adjacent  \ibrate  inward.  In  I'dg.  48  the  linger 
lias  l)een  ])re>>ed  against  one  corner  of  the  ])late.  while  in 
I'ig.  4*^  two  other  points  have  also  been  touched.  When  the 
plate  i.>  di\'i(led  as  in  hdg.  47  the  fundamental  is  sounded, 
ddie  di\dsion  .-hown  in  I'dg.  48  gi\-cs  a  tone  a  lifth  higher;  and 


+ 

». - 

+ 

FiL'.    47. 


Fig.    48. 


Fig.    49. 


more  comi)licated  divisions  result  in  tones  still  more  acute  in 
pitch.  15y  touching  the  ])late  at  ^■arious  other  piMUts  a  multi- 
tude of  beautiful  figures  ma\'  be  evoked,  such  as  those  shown 
in    I'dg.    46. 

W  hen  the  plate  is  strewn  with  a  very  light  material,  such 

a-;  lycopoditmi  powder,  the  effect  of  the  vibration  U]V)n  this  is 

e.\actl\-   the   oi)i)o>ite   of    what   it    \\as   upon   the 

Effect  on  light  "   .  '  '  ' 

powder  of  vibra-     saud,  suicc  the  powdcr  collects  at  the  centre  oi 

tion  of  plates.  .,.,,,  „,, 

the  segments  instead  ot  along  the  nodes.  I  he 
reason  for  this  fact  is  that  the  e-xceedingl}-  light  particles  are 
drawn  int*)  the  vortices  of  the  minute  whirlwinds  which  are 
generated  b\-  the  \ibrating  ])ortions,  and  so  are  heaped  uj) 
upon  the--e  latter. 

Compound  sand  figures  liave  been  i)roduced  by  ])lacing  one 
plate  <)n  top  of  another  in  >uch  a  wa\-  that  \-ibrations  of  O{)])o- 
^,       ,,  site  phases  were  superimi)osed.     Circular  platc< 

Other  plate  '  '  '  ' 

figures.  (,,-  disks  also  give  rise  to  other  interesting  sanrl 

designs,  which  follow  the  .-^ame  general  laws  as  those  govern- 
ing <r|uare  i)lates. 

A  bell  ma\-  lie  regarded  a-  simpK'  another  form  oi  disk. 
Where  the  hammer  strikes  the  side  of  a  bell  a  ventral  segment 


SOUND.  .IND  ITS  RELATION  TO  MUSIC 


63 


Partials    of 
bells. 


Fig.    SI. 


is  formed;  and  when  ihc  fundamental  is  sounded 
the  bell  divides  into  four  of  these  segments, 
se])arated  by  nodes.  V\\^.  50  shows  a  glass  bell  against  the 
(.'iV^L'  of  which,  at  e(|ual  distances,  ivory  balls  are  suspended. 
When  these  touch  the 
nodes  thev  remain 
nearly  (juiet ;  but 
when  they  are  in  con- 
tact with  the  seg- 
ments thev  are  forc- 
ibly repelled,  ddiese 
divisions  are  again 
shown  on  the  surface 
of  the  water  in  the 
glass  bell  .  /  pictured 
in  big.  51,  where  the  nodal  lines  /  c  and  (]  h  intersect  the 
agitated  parts  of  the  surface  and  the  maximum  disturbance 
is  at  a.   b.   c  and  d. 

-Maiu  inharmonious  partials  would  be  elicited  from  a  bell 
of  uniform  curvature  and  thickness;  and,  to  avoid  these, 
various    shai)es    and    materials    have    been    em-    _     ,.    .,. 

I  Peculiarities 

ployed.  Famous  makers  like  \  an  der  Gheyn  °^  '^^"^■ 
(1550)  and  llemonv  (1650)  have  formulated  laws  and  pat- 
terns which  are  generally  observed  by  bell  founders.  The 
fact  that  the  segments  of  large  bells  are  seldom  in  perfect 
unison  with  one  another,  owdng  to  slight  unevenncsses  in 
construction,  causes  the  frequent  presence  of  beats  (page  47). 
Strctclicd  incinbrancs  are  ])ractically  plates  of  great  tenuity 
and  flexibilit}'.  While  possessing  similar  pro])erties  of  form- 
ing nodes  and  segments,  their  extreme  sensiti\-    „    .•  i     r 

'^  -^  Partials  of 

ity    and    power   of    producing   almost    an\-    series    membranes, 
of   vibrations  makes  them  valuable  as  agents  of   sound-trans- 
mission ( i:)age  82).     ddieir  musical  uses  are  chiefl\-  in  connec- 
tion  with  instruments  of  percussion. 

Confined  (^ort'io}is  of  tlic  air  or  of  (/ases  mav  be  made  to 
emit  sounds  of  great  musical  beauty.  All  the  wind  instruments 


64  SOUXD.  ,1XD  ITS  RliLATIOS  TO  MUSIC 

„  ,  of    the   orchc.-tra.    indeed,    are   offshoots   of    tliis 

Tones  of 

sonorous  tubes.  plKiiomcnon.  The  principles  on  which  these 
in>trunients  are  ])a>ed  are  the  same  as  tliose  which  gcjvern 
tlie  tones  of  sonorous  tubes,  which  we  now  ])rocced  U)  consider. 
That  it  is  reall\-  the  air  witliin  these  tubes  winch  vibr;ite.- 
and  not  the  solid  exterior  walls  can  be  easilv  shown  bv  ex])eri- 
mentini''   with    three    tubes    of    exactl\-    the    same 

Proof  that  the  .  '  .  . 

air  in  a  tube        sizc    but    ot    (littcrent    materials,    ,-uch    as    glass. 

'''^'■^"^-  1  11  1        I         -11    1        -         i'     1 

cop])cr,   and   cardboard.      It   wnl    Ije    l<jund   that 

the  tones  of  all  three  are  practicallv  identical,  and  therefore 

independent  of  the  com[)osition  of  the  tube  itself. 

Taking  now  a  tube  elosed  at  one  end   i  big.  ?2).  we  set  the 

encloscfl  air  into  \'ibration  l)v  blowing  gentl}'  across  the  o]X'n 

to]).      lmmedialel\-  a  ])ulse  of  condensation 

A    sound-wave  .  '  . 

in  a  stopped        passcs    troui    (/    througli    b.    and   e,    and    is 

tube.  1111 

reflected  back  at  a.  An  accomjjan}  ing 
pulse  of  rarefaction  follows  the  same  cour>e.  so  that 
the  tttbe  is  tra\"ersed  lengthwise  four  times  in  the  ])a>sage 
of  a  single  sf;und-wa\-e,  (jr,  in  other  wrjrd^,  each  sound- 
wave is  fcnir  times  the  length  of  the  tube.  I'.v  Idling 
the  tube  with  various  gases,  tones  of  different  pitches  are 
produced.  Since,  however,  their  sound-waves  are  all 
equal  in  length,  the  relati\"e  velocit}-  of  sound  in  the  air 
and  in  the-e  gases  can  Ije  easil\-  calculated.  Fig'~T2. 

At  the  end  d.  where  there  is  the  greatest  alternate  conden- 
sation and  rarefaction,  there  is  _\"et  the  least  motion;  hence  a 
node  is  formed  across  the  tube  at  this  ])oint.     A 

Upper    partials  .  , 

of  stopped  maximum  ot  movement  mu-t  aUvavs  take  ])lace. 

i^^^^-  ,  1  1  1  •  1    •'      1  1 

liowever.  at  the  o})en  end  a.  which  is  thus  alwaws 

the  middle  of  a  \'entral  segment.  \\  hen  the  air  in  the  tube 
\ibrates  under  a  more  })owcrUil  current,  the  tirst  U])per  ])ar- 
tial  is  formed;  and  the  additional  node  is  a  third  of  the  length 
of  the  tube  from  its  to]),  just  as  was  the  case  with  a  rod 
fixed  at  one  end.  In  like  manner  the  succeeding  partials  are 
formeri  b\-  rlivisions  of  the  tube  according  to  the  odd  num- 
bers, .r  .^.  7.  and  so  forth,  as  shown  iii   I'^ig.  .^.x     These  r)artials, 


SOUND,  .IXn  ITS  R/iLATfOX  TO  MUSIC 


65 


•; 


unlike  those  of  rods  fixed 
at  one  end,  are  members 
of  the  harmonic  series  of 
strings    (  I'lg.  27). 

Tubes  o['cn  at  both  ends 
iin'olve  conthtions  some- 
what (Hii'ercnt  from  those 
just  discussed.  A  pulse 
of  condensation  entering 
such  a  tul)e  (  h^ig.  34)  at 
a.  passes  through  c  to  b, 
where  it  rushes  out  into 
the  free  air,  generating  at 
the  same  time  a  pulse  of 
rarefaction,  which  starts 
back  from  /.'.  Another 
pulse  of  rarefaction,  how- 
ever, starts  simultaneously 
upward  from  a  at  the  same 
rate  ;  and  the>c  two  pulses,  encountering  each  other  at  e  with 
e(|ual  force,  Icnvc  the  air  at  c  in  a  state  of  rest,  or,  in  other 
words,    form    a   node   there,    each   of    the    .  , 

'  A  sound-wave 

])ulses  then  rushing  by  to  its  destination  '"  ^"  °''^"  '"''^• 
at  the  end  opposite  to  that  from  whence  it  came.  Pulses 
of  condensation  now  start  back  from  each  end,  meeting 
at  the  nodal  ])lane  c  as  did  the  pulses  of  rarefaction. 

It  is  evident,  therefore,  that  a  com])lete  sound-wave 
involves  the  passing  of  a  pulse  of  condensation  from 
a   to  /'   and  a  return  of  a  pulse  (^f  rare- 

.  .  Length    of    a 

faction   from   b  to  a,  or,  m  other  words,   sound-wave  in 

-      1  ,         .         ,  ,      an  open  tube. 

a  length  of  twice  that  ot  the  tube  itself. 
Inasmuch,  however,  as  the  length  of  a  sound-wave  in  a 
stop])ed  tube  was  four  times  the  length  of  the  tube,  it 
follows  that  an  open  tube  must  give  a  fundamental  tone 
an  octave  higher  than  that  of  a  stepped  tube  of  the  same 
length,  since  its  sound-wave  is  only  one-half  as  long. 


Fig.   S3. 


FiK 


66 


SOrXD.  .IXD  ITS  RJiL.l'JIOX   TO  MUSIC 


With  the  formation  of  upper  jiarlia!^  in  an  open  lube,  both 
ends  of  the  tul)e.  where  the  l)(Jint^  of  maximum  minion  art- 
located,  will  alwa\"s  l)e  centres  of  ventral  >ey- 
ments.  When  there  are  two  no(le>,  forming'  the 
secrind  partial,  an  entire  segment  will  C(jnsequently  arise  in 
the    middle   of    the   tube,    and    a   half    segment    at    each    t-nd ; 


Partials  of 
open  tubes. 


/    \ 


Fig.    56 


hence  the  nodes   will   ' 
from  each  of  its  end.-. 


)e  a  c|uarter  of  the  lengtli  of  the  tube 
The  tone  thus  gi\en  out  i.-  an  octa\e 
above  the  fundamental.  The  third  ])artial.  >ound:ng  an  octa\'e 
and  ;•.  lifth  al)OVL'  the  tundamcntal,  lias  node:-  one--i.\th  of 
thit  len^^tli  from  the  ends  and  al>o  a  node  in  the  middle;  while 
the  i"i  iurih  ])artia].  -iiunding  two  octa\e.N  ,ibo\-c  the  ftmda- 
meiual.  Iia--  nodes  one-eighth  of  the  length  from  each  end, 
\sith  two  iither<  at  ecjual  di>tance>  between.     .All  the-^e  utTect- 


SOl'Xn.  .1X1)  ITS-  h'HL.ITfOX   TO  Ml  SIC  67 

arc  shown  in  Vig.  55.  The  ii])i)cr  ])artials  in  this  case  follow 
the  harmonic  scries  inibrokenly  in  the  snccession  i,  3,  4,  o 
and   so  on. 

A  clear  method  for  showing"  the  position  of  the  nodes  in 
tubes  open  at  both  ends  is  shown  in  My.  56,  where  such  a 
ttil)e  is  represented  1)\-  an  o])en  organ  ])ipe  P  P, 

Location  of 

having  one  of  the   sides  made  of  glass,      if  this    nodes  and 

sc2f  mcnts. 

pipe  be  ptit  into  \ibration  and  a  small  strcu'hed 
mcml)rane  in   strewn   with   sand  be  lowered   into  it,  the   sand 
will  dance  about  where  the  motion  is  greatest,  but  will  remain 
(|uiet  when  a  node  is  reached. 

Tubes  of  which  the  length   is  great  in  proportion   to  their 
diameters   follow  (|uite  closely  the  law   suggested  above,   that 
the    pitch    is    inversely    proportional    to    the 
length    of   the    tube.      The    i)itch    may    be    con-    Modificaiions  of 

°  I  J  ^  theoretical  laws. 

siderably  affected,  however,  by  greatlv  increasing 
the   diameter.      \'ariotts   other   conditions   as   to   the   shape  of 
the  tube  cause  modifications  of  its  the(n-etical  laws,  and  must 
be  taken  into  consideration  by  instrument  makers. 


6S  SOUND,  AND  ITS  RELATION  TO  MUSIC 

SUMMARY 

The  quality  of  a  tone  depends  upon  the  number,  position, 
relative  intensity  and  i)hases  oi  the  secondar}-  tones  which 
are  mingled  in  it.  The  relation  of  these  upper  partials,  as  lhe\' 
are  called,  to  the  fundamental  ma}'  be  expre>sed  by  sim])le 
whole  numbers,  in  which  case  the\-  are  called  harmonic  ])ar- 
tials,  or  bv  fractional  numbers,  when  the\-  are  called  inh.ar- 
monic  partials.  Given  com])lex  tones  can  be  reconstructed 
only  in  scj  far  as  the\-  contain  the  sim])Ie  harmonic  jjartials. 

In  forming  their  ])artials  \'ibrating  bodies  divide  U])  into 
nodes  and  ventral  segments.  The  presence  of  several  ])artials 
causes  complicated  motions  in  the  \-ibrating  body.  Strings 
form  their  ])artials  in  an  harmonic  series,  the  members  of 
which  are  related  to  each  other  as  the  successi\e  simple  whole 
nimibers.  The  partials  of  rods,  plates  and  membranes  are 
generally  inharmonic  and  high-pitched.  The\'  are  formed 
under  various  and  scjmetimes  com])licate(l  ccnulitions. 

Tubes,  either  stopped  at  one  end  or  oi)en  at  both  ends,  give 
out  musical  tones  bv  the  vibrations  of  the  air  or  gases  with 
which  they  are  filled.  While  in  both  cases  the  harmonic  series 
of  partials  is  produced,  in  that  of  stoi)])ed  tubes  onlv  the  odd 
])artials  are  possible,  while  the  entire  series  can  occur  in  tubes 
(j])en  at  both  ends. 

l^EI'Kr^F.XCE  LIST. 

Ilelmlioltz.  Chapters  5,  6. 

Tyndall.  Chapters  3,  4.  5,  6. 

Zalnii.  Chai)ters  4,  5.  6.  9. 

I'cyiUiiii/  and  I'hoiiipscii.  Cliaj^ters  5,  6,  7,  8. 

Inmics.  Chapters  3,  (>.  7.  8, 

Harris.  Chapters  8,  9,  10,  11. 

Taylor.  Chapter  4. 

Bruail house.  Chapter  8. 

Stone.  Cha[)ter  5. 

Laiifpiac.  Cliapter  1.  A. 

Barton.   Chapter  5. 

HIascrna.  Cliapter  8. 

f'olc.  (Jhai)ter  3. 


CHAPTER  VI 

Ri'.soxAXci': 

XoT  only   do  sounding  bodies   transmit   their  vibrations   to 
tile   surrounding   atmosphere,    but   tlie\-    also   have   the   i)o\ver  v 
of    setting    ui)    svmimthetic    vibrations    in    other    „,      , 

■^         i         -        1  The  phenomena 

bodies,  whether  these  latter  are  in  direct  coiUact   °^  resonance, 
with   them   or  not.      I^Vom  these   conditions   man\'   interesting 
results   follow  which  are  grouped  together  under  the  title  of 
the  phoioinciia  of  rcso)iancc. 

To  understand  the  nature  of  these  phenomena,  we  must 
recall  the  familiar  mechanical  law  of  cumulative  impulses. 
'Jdie  working  of  this  law  may  be  illustrated  bv  „,    ,       , 

'^  -'  -      The  law  of 

an  old-fashioned  swing,  well-freighted  with  chil-   cumulative 

"'  o  impulses 

dren.  Another  child  stands  behind  the  swing-  illustrated, 
seat,  and  when  he  gives  it  a  slight  push  it  swa\'s  gently  awav 
from  him,  immediately  returning  in  his  direction.  A  second 
])ush  increases  the  momentum,  which  grows  still  greater  as 
the  pushes  continue,  until  the  children  are  flying  through  the 
air  in  long  sweeping  undulations,  to  their  great  delight.  Each 
j)ush,  howe\-er,  must  be  given  exactly  as  the  swing-seat  reaches 
the  point  nearest  the  pusher  in  order  to  be  eiifective,  since 
otherwise  its  motion  would  be  retarded  or  might  even  be 
entirely  stopped. 

For  another  illustration  of  this  law,  let  a  heavy  weight  such 
as  a  cannon  ball  be  suspended  from  the  ceiling  by  a  string,  and 
let  a  slender  thread  be  attached  to  the  weight. 

Further 

r>v  gentlv  pulling  upon  this  thread  at  the  ])r()per    illustration 

11  -1  i_-        11  1  1  of   the   law. 

intervals    the    weight    may    hnally    be    made    to 
oscillate    back    and    forth   over   a   considerable   arc.      A   more 
remarkable   form  of  this  experiment  is  performed  bv  simplv 
blowing  puffs  of  breath  against  the  weight,  which  may   thus 
be  induced  to  assume  a  motion  almost  as  great  as  before. 
Similar  results   follow  when  a  ship   is  tossed   about   in   the 


7('  souxij,  AXD  iT.->  ri:latiu.\  tu  music 

irouyii    of    the    sea,    gaining    momentum    from    the    continued 
imi)ulses    of    even    comijaratix  elv    small    waves. 

Practical  ,  .  . 

examples  of  Suldiei"-,    wlieii    marchuig    across    a    bridge,    are 

the  law.  ■  '. 

commanded  to  break  ste]).  >ince  otherwi-e  the 
results  to  the  structure  fronrtbe  accumulated  momentum  might 
be  disa.^trous. 

We  ma\'  a])})rcKich  the  musical  ai)plication  '>i  this  law  b\ 
a  few  e.\i)eriments  with  ordinar\-  pendulums.  Let  two  oi 
Transference  of     the>e    wliich    luu'e    tile    >ame    \"il)ration    rate    be 

pendulum  ,      ,     -  ,  •  ,  i  -  -      , 

vibrations.  -u^jieiuled  t roni  a  bar  ot  wo.^d.      It  one  ot  them 

-a)    When    the  .  .  .  .,,  .  . 

pendulums  have    be   HOW    sct   lu    motioii    ii    Will    commuuicate    lt> 

the  same  ■,  ■  i  i  i  i       i 

vibration  rates.  Vibration.'-  to  tile  otHLM"  thrtjugb  the  comiiKjii  sup- 
])orting  bar,  so  that  liotli  will  o.-^cillate  alike.  I'urther  than 
tlii-,  if  two  clocks  whose  pendtilums  \-il)rate  ali)u>st  exactl}"  in 
ihe  .-ame  time  be  set  side  by  side  on  a  table,  the  f|tucker  of 
tlieiii  will  draw  U])  the  time  of  the  other  until  the}"  mo\'e  in 
iini-(  m. 

In  the  case  of  the  swing  abo\e  alluded  tc),  if  the  child  had 
gi\"cn  a  ])U>h  at  the  expiration  of  e\er\-  two  o-cillations  instead 
,,  ,   ,,,,       .,        ^if  each  one.  the  nionK-ntum  would  ha\e  increa>ed 

(b)    When    tne 

pendulums  have    .^^   before,  but   iiKjre   slowlv.      With   one   pudi   to 

dinerent  vibra-  -  ' 

tion  rates.  cacli    three    o>cillations    the    iiiolioii    would    ha\'e 

auumented  still  more  slowly,  and  with  one  ini-h  to  each  f^air 
I  i-cillatii  ins  the  incr(ja>e  would  have  I)een  \'erv  -low  indeed, 
."^o,  if  (tiie  of  two  pendulums  attached  to  ;i  common  liar  \-ibraie- 
twice  ci<  slo\vl\-  a-  the  other  it  will  .--et  the  latter  in  vibration 
b\-  ;id(ling  to  il-  momentum  at  e\"er\-  -ecoiid  >wing  :  but  this 
el'ect  will  I'ccur  more  gradualK'  than  wa-  the  ca-e  when  tlie 
jieiululum  had  tile  <anie  vibration  rate.  .\  corropi  iiiding 
]e--ening  of  iiitluence  will  take  ])lace  if  the  first  ])enduluni 
lia-  a  vibration  rate  one-third  (>\-  one-fourlh  that  (jf  its  c^  aii- 
])ani'  >n  ])enduluin. 

Let  u-  111  iw  hold  in  either  hand  one  (^i  two  tuning- lork- 
whitdi  lia\e  exactL'  the  -ame  viliration  number.  Striking  i  iiie 
of  the-e  and  soon  alter  damping  it  with  the  fmger-.  we  are 
:ibl(,-  111  hear  a    faun    re-])oii-e  coming"   from   the   iither       If   llie 


SOl'XD.  .IXIJ  ITS  RliL.lTlOX   TO  MC.^IC 


xihratidii  numlicrs  of  tlic  two  forks  were  not  the  same,  no 
such  tone  would  be  ])rocluce(i.  When  llicse  are  ecjual.  how- 
e\er,  the  fork  originally  sounding  impinges  its 

^  ^  &  i-       &  Sympathetic 

vibrations  upon  the  other  through  the  medium    vibrations  of 

,      .  .         ■  .  tuning  forks. 

of  the  air,  ju-^l  as  uie  pushes  were  .i^iven  to  the 
-win.i;-,  or  the  ])urf>  of  lireath  struck  tlie  suspended  cannon 
hah.  A  inilse  of  c(jn(len>ation  prtjceedin^'  from  tlie  lirst  fork 
hits  tlie  second,  giving  it  a  slight  forward  momentum.  It- 
return  is  then  facilitated  1)\-  coincidence  with  the  rarefacti(jn 
which  ha<  folhnved  the  condensation  from  the  lirst  fork. 
.\nother  pul-e  of  condensation  now  strike-  the  second  fork, 
and  the  whole  ])rocess  is  rei)eated  with  slightly  increased 
momentum.  Thus  the  motion  accumulates,  as  in  the  exam])lcs 
above  cited,  until  the  ,-econd  fork  sings  stcadilv  with  the 
tirst. 

Hut  a  tuning-fork  ma}"  with  equal  facilit\-  incite  s}'mpathetic 
\ibrations  in  bodies  unlike  itself.  Let  us  hold  our  sounding 
fork  o\er  a  gla-s   iar.  as  in    biij".   r7 ,  tirst  ascer-    „„    .    , 

■^  •'  ^  Effect  of  a 

taining  the  pitcli  of  the  air-column  in  the  emptv    tumng-fork 

'^  '  '     -       upon    an    air- 

jar  1)^-  ])lo\ving  gently  acr(jss  its  mouth.      If  this    column. 

l)itch   is   higher  than   that  of   the   fork   it   will   be  necessar\-   to 


iwer  n  h\- 


hading,"'  which  is  accoiuplished  ])y  ])artl\-  clo-ing 
the  mouth  of  the  jar  with  a  card 
or  other  flat  object.  If,  howex'er. 
the  p'lich  f)f  the  jar  i>  lower  than 
that  of  the  fork,  water  may  be 
poured  in  until  their  \ibration  num- 
bers coincide.  Tlie  point  at  whicli 
the\-  are  in  uni-or.  ma\-  be  easily 
determined,  since  the  tone  of  the 
li         !  fork    will    become    reinforced    b}* 

I'         '  the  resonance  of  the  air  in  the  jar 

when  the  vibration  numbers  ap- 
proach each  other  closely,  and  this 
resonance  will  attain  a  maximum 
when  they  are  exactly  the   same. 


72  -OUXJJ,  JXD  ITS  KLLATIOX  TO  ML' SIC 

Under  the  latter  condition  what  takes  place  is  as  follows: — 
When  the  prong  of  the  fork  moves  to  h  (Fig.  h7 )  a  pulse  of 
„    ,      ^.       c      condensation    runs   down   the    iar   as    far   as   the 

Explanation  of  ^     ^     i 

this  effect.  water  level,  whence  it  rebounds ;  and   when  the 

prong  moves  to  a  a  pulse  of  rarefaction  performs  the  same 
process,  the  entire  sound-wave  thus  equaling  four  times  tht 
distance  from  the  mouth  of  the  jar  to  the  water  level,  as 
might  be  expected  in  the  case  of  a  tulje  stopped  at  one  end 
( l)age  64).  Knowing  the  vibration  rate  of  the  fork  we  may 
now  calculate  what  should  he  the  length  of  the  air-column 
in  the  jar.  If  the  fork  gives  435  vibrations  ])er  second  to  a'. 
for  instance,  the  length  of  its  sound-wave  must  ecjual  the 
velocity  of  sound  ])er  second,  or  1120  feet,  divided  bv  435, 
and  the  length  of  the  air-column  must  conseciuently  be  aljout 
seven  and  one-half  inches,  which  is  one-fourth  of  the  result 
of  this  division.  In  the  case  of  a  tube  open  at  both  (znd^ 
the  air-column  is  twice  as  long,  or  about  fifteen  inches  \\'e 
may  test  the  accuracy  of  these  conclusions  by  rolling  up  a 
piece  of  cardboard  so  that  it  forms  a  tube  fifteen  inches  long 
and  an  inch  in  diameter,  and  holding  over  one  end  the  sounding 
fork,  when  the  tone  should  swell  out  considerably.  I-^xtending 
or  diminishing  the  length  of  this  tube  will  reveal  the  condition 
of  greatest  resonance. 

It  was  noted  that  the  tone  of  the  fork  begins  to  be  rein- 
forced a  little  before  the  point  of  maximtim  resonance  i-- 
„,        .  ,    ,        reached.     Idiis  result  occurs  from  the  fact  that 

The   point   of 

reinforcement        j]^^,   flexible   character  of   the   air-column   allows 

or    the    tuning- 

^°^^-  it  to  be  more  easilv  influenced  than  the  more  rigid 

ttming-fork,  which  required  absolute  tmison  with  another 
sounding  bodv  before  it  could  be  affected  by  it. 

Savart  devised  an  apparatus  shown  in  Fig.  58  which  vividly 

illustrates    the    phenomena    of    resonance.      .V    l)ell    T    /'    is 

mounted  on  a  stand  /)  V  C  to  which  is  altached 

Savart's  .  ,  ,  i         t  i   •  i  i 

resonating  at  B  a  rcsouating  chamber  ./.     In  this  chamber 

device. 

is  a  ])iston  which  pro\'i(les  for  the  regulation  of 
its  lens^th.     When  the  bell  is  sounded  1)\-  a  \-iolin  bow  and  the 


SUL'XI),  .-IXI)  ITS  RliL.rnOX  TO  Mrsic 


|)i>l(in  is  moved  back  and   forth  the  varying  degrees  of   reso- 
nance are  perceived,  the  niaxiniuni  sounchng  with  great  power. 
Resonating  chambers  sncli  as  this  are  sometimes  attached  to 


Fig.    58. 

tuning-forks  to  heighten  their  effects.     More  often,  however, 
the    forks   are   mounted    upon    resonating   boxes  Resonating 
which    are    constructed   of    a    size    calculated    to    boxes. 

insure  the  best  results,  and  which 
are  left  open  at  one  or  both 
ends.  I'hus  a  fork  having  a 
vibration  rate  of  384  requires  a 
box  open  at  one  end  only,  having 
a  length  of  7.3  inches,  a  width 
of  3.8  inches  and  a  depth  of  1.8 
inches.  A  fork  thus  mounted 
is  shown  in  l-'ig.  59. 

15v  ex])erimcnting  with  two  re- 


^^ 


Fig.    59. 

inforced    forks   of    the    same   vibration    rate   some    interesting 
results  mav  be  obtained.      l?lacing  them  a  short 

...  ^  ,  .     ,      .         Experiment 

distance  apart  and  pouUmg  the  open  ends  ot  their    with  reinforced 

,111  1      tuning-forks. 

resonatmg  boxes  toward  eacii  other,  let  us  sound 
one  of  the  forks  b\-  a  violin  bow.     Immediately  the  other  re- 
sponds with  a  strong  tone,  which  continues  after  the  first  one 
is  damped  with  the  fingers.     If  we  now  release  the  first  fork 


74 


SOi'XD,  .L\'D  ITS  RliLATIOX   TO  Mi' SIC 


and  afterward   damp   the   second,   the   hrst   will   again   sound. 

having  taken  its  motion  from  the  second;  and  this  proces>  of 

transference  may  he  repeated  until  the  energy  (jf  the  \-ibration- 

is  entirely  exhausted.    .Again,  if  one  of  the  forks  be  put  slight]}- 

c)Ut  of  tune  with  the  other  by  attaching  a  i)iece  of  sealing  wax 

to  one  of  its  prongs,  it  will  still  respond,  since  the  \'ibrati(>n- 

will  be  transmitted  through  the  resonating  boxes,  although  the 

response  will  be  much  feebler  than  at  first. 

While  we  originally  placed  the  unison   forks  near  together, 

>uch  proximitv  is  not  necessary,  since  if  \\'e  sepcirate  them  b\- 

the  length  of  the  room  thev  affect  each  (jther 
Effect  of  *  -.  .  . 

distance  upon       nearK"    as    ])owertullv    as    betore.      Dr.    Kot-mg 

resonance.  '  .  .  '  .  .       ,  .     ' 

made  some  mterestmg  cxpernnenis  on  tins  line 
with  two  tuning-forks  each  ha\'ing  a  vibration  rate  of  12S 
per  second,  througli  the  conduit  of  Saint  Mi(-hel,  in  Pari- 
\W  pointing  the  o])en  ends  tif  their  res(Tnating  l)0xes  toward 
each  other  he  was  able,  upon  sounding  one  of  them,  to  elicit 
a  response  from  the  other  at  a  distance  of  o\er  a  mile. 

\\hene\'er  a  ljod\'  is  free  t(j  \'ii)rate  in  uni-on  wiih  a  >ouiid 
ing  body  in  its  \'icinitv  such  s}-m])athelic  \'il)rations  will  be  -el 

U]).      If   the  two   strings  of  the   S(jnometer    i  l-^ig. 

Conditions  -, -,        ,  ,      •  ■"  i  -       ,  ,' 

favorable  to  JJ  1     be    tuucd    m    uuisou    and    one    ot    them    he 

resonance.  111,  1  -ii  i        \\-       1 

plucked,  the  other  will  re>])on(l.  We  na\e  orteii 
felt  the  vibrations  of  an  entire  edifice  when  it  acted  in  -ym])alhy 
with  a  deep-toned  organ  jjipc.  A  tone  siamded  on  the  ])iano 
mav  cause  a  chandelier  ()r  a  ^\■indow  pane  to  jingle  ^•iolentl_\. 
The  writer  was  once  ])laving  ujjon  the  ])iano  when,  from  tlie 
force  of  a  loud  lone  to  which  it  re-i)on(led.  a  large  bowl  of 
hea\w   ghi'-^   in   an   adjoining   room   was    shallered. 

Pig.  oO  shows  a  device  called  a  si.iind-iniU .  in  which  mechan- 
ical use  is  made  of  reso- 
nance. b(jur  small  cylin- 
ders each  open  at  one  end  are  atlached 
lo  radiating  arms  balanced  U])on  a  cen- 
tral pi\ot  so  that  the_\-  re\-ohe  freelw 
When    ihe    lone    to    which    lhe\-    ;ire    all 


The   sound- 
mill. 


SOiWD.  JXD  ITS  RliLATIOX  TO  MUSIC 


/o 


tuned  is  sounded  the  pressitre  upon  the  node  at  tlie  bottom 
of  each  causes  them  to  rotate  as  long  as  tlie  sound  continues. 
Xo  motion  will  he  produced  unless  the  actuating  tone  he 
absolutely  in  unison  with  that  to  which  the  cylinders  are 
tuned. 

'ihe  resonators  devised  bv  1  lelmholtz  have  already  been 
described  (page  ?1).  J'^ach  of  these  instruments  has  the 
power  of  selecting  oiu  one  simijle  tone  to  which    ,,    .        . 

1  '^  '  Various     iorms 

it  responds.  Other  forms  of  resonators  have  °^  resonators, 
also  been  invented  which  mav  be  adjusted  to  more  than  one 
tone,  or  which  ma\-  res])t)n(l  to  several  tones  at  once.  Per- 
haps the  most  startling  results,  however,  are 
produced  bv  an  in>trument  of  this  species  which 
reinforces  the  murmuring  sounds  c(jnstantlv 
tiitting  about  in  the  atmosphere,  but  which  are 
ordinarily  imi)erceptible  t(_)  the  ear.  ]n  the  form 
of  a  straight  trumpet  with  a])ertures  in  the  sides 
for  changing  its  resonating  ])itch,  this  mclodia- 
pho)ic.  as  it  is  called  i  b'ig.  61  ),  when  adjusted 
to  the  ear  permits  (.)ne  to  hear  a  succession  of 
tones  which  are  thus  raised  frcjm  insignificance 
into  power.  The  singing  of  the  seashell  when 
it  is  lield  to  the  ear  furnishes  another  ilhislration 
^'^-  ^'-  of  the  same  princijjle. 

In  the  case  of  wind  instruments,  which  are  really  tuljes  t)f 
\ariotis  sizes  and  shapes  either  sto]:)ped  at  one  end  or  open 
at  both  ends,  the  air-columns  are  set  into  \-ibra- 

,  ,  ...  Resonance   of 

tion  m  one  ot  two  wa\"<,  the  tn"st  ot  which  is  bv    wind   instru- 

...  .'       .  ,  '       ments. 

directing  a  stream  ot  air  toward  a  sharp  edge 
at  the  mouth  of  the  tube,  and  the  second  bv  causing  a  reed 
annexed  to  the  air  chaml)er  to  \-ibrate.  F.xamples  of  the 
former  method  are  found  in  flutes  and  the  flue  pipes  of  the 
r)rgan.  while  the  latter  is  exemplified  in  clarinets,  oboes  and 
the  reed  j^ipes  of  the  organ. 

The  exact  manner  in  which  \il)rations  are  incited  in  pi])es 
of  the  flue  or  ■"whistle"  t\'pe  is  still  a  subject  of  contro\-cr-\-. 


76 


SOiWD.  AXD  ITS  RELAllUX  TO  MUSH 


How  flue 
pipes  are 
made  to  speak 


I'iy".  ()1  represents  a  section  of  an 
organ  pipe  of  this  kind.  In  tliis 
tlie  air,  forced  from  tlie  wind  che<t 
throLii^ii  tlie  tube  a.  enters  tlie  cliamber  h. 
whence  it  ru-he>  in  a  thiii  sheet  througli  tlTc 
small  a])erture  c  toward  the  sharp  edge  at  (/. 
Helinholtz  a>>erted  that  the  hissing  ncjise  made 
at  this  point  is  caused  1)\-  a  mixture  of  tone-; 
to  one  of  wliich  the  pipe  responds  by  resonance. 
A  later  theor\-  which  has  met  with  mtich  a])- 
I^roval  is  that  the  thin  layer  of  air  directed 
across  the  embrochtire  d  c  acts  like  a  reed  and  so 
in\-igorates  the  air  in  the  large  chamber  of  the 
pipe.  The  general  and  sectional  view  of  a 
wooden  organ  ]ii])e  in   h^ig.  63  and  of  a  metal  one  in 


. 

^; 

Fig.    62. 

I'i-.  ^4 


Fig.    63. 


Fig.    64. 


shows  the  structure  of  the.^e  and  the  i)osition  of  the  air-inlets. 
A   reed  i)r(j])erh-  consists  of  a  thin,  narrow  stri])  of  flexible 


b  -».^  b 


SOUWD,  AND  ITS  RIlLATIOX  TO  MUSIC  77 

flialcrial,  llxcd  at  one  end.     Organ  reeds,  commonly  of  metal, 
\il)rate  over  a  rectangular  orifice  either  slightly    construction 
narrower  and   >h()rler  than   the   free  part  of  the    °^  reeds, 
.•eea  itself  or  just  large  enough   to  permit   the  reed  to  move 
within  it.     In  the  former  case  the  vihrating  reed  hits  the  sides 

of    the    orifice    and 
l^^^^y    -  -----  -    "--'^^^'"^''^I^I/'^St;;;^  is  called  a  strikiiuj 

^    a%:       '. ^  .     -     "  "         '      ',        reed,    while    in   the 

latter  case  it  is 
called  a  free  reed. 
The  top  and  side 
views     of     a     free 

FiR.    65.  J  •  • 

reed  are  given  m 
hig'.  ()3.  The  tongue  r  .c  is  attached  to  the  metal  block  a  a, 
^■ibrating  between  the  positions  at  j::^,  and  c._,,  B.  The  air, 
l)assing'  in  the  direction  of  the  arrows,  is  emitted  in  a  series 
of  ])uffs  similar  to  those  of  the  siren.  Since  the  resulting-  tone 
is  very  rich  in  up]ier  partials,  some  of  which  produce  a  strident 
effect,  it  is  necessar\-  for  musical  i)uri)oses  that  one  of  the  tones, 
most  often  the  ftmdamental,  should  be  so  reinforced  as  to 
overcome  the  presence  of  these  discordant  elements :  hence 
the  reed  is  generallv  ttsed  in  connection  with  some  form  of  a 
resonating"  tube.  Idie  fact  should  be  especially  noted  that  the 
tone  of  the  reed  is  caused  by  the  puffs  of  air  to  which  it 
gives  rise,  and  not  by  the  vibrations  of  the  tongue  itself. 

Examples  of  the  use  of  both  free  and  striking  reeds  in 
organ  pipes  are  pictured  in  Fig.  66,  .  /  illustrating  the  former 
and    B    the   latter.      A    conical   tube    such    as    is    .^       ,       ,    . 

Use  of  reeds  in 

shown  at  the  top  of  the  i)ipe  .  /  is  frecjuently  ^'^^^'^  '"p^^- 
superimposed,  in  various  shapes,  to  modifv  the  (|ualitv  of  the 
tone.  I'\)r  changing  the  ]Mtch  of  the  reed  a  tuning  wire, 
which  presses  against  it,  ma\'  shorten  the  vibrating  ])art,  thus 
raising  the  ])itch,  or  may  lengthen  it,  with  the  opposite  result. 
In  /?  the  air  rises  into  the  large  chamber  through  the  tube 
at  the  lower  end.  Passing  into  the  semi-cylindrical  tube  r  r. 
which  is   fastened  to  the  block  .s-  ,9,  it  sets  into  vibraticMi  the 


78 


SOUND,  AND  ITS  RI-L.ITION  TO  MUSIC 


reed  i,  which  causes  the  air 
in  the  chamber  to  sound 
hy  sympathetic  vihraticMi. 
bov  this  latter  resuh  to 
occur  it  is  necessary  that 
the  air-column  in  the  cham- 
ber should  be  at  least  nearh 
of  the  same  pitch  as  the 
reed  itself.  Since  the  reed 
is  of  metal  and  therefore 
of  considerable  rij^iditw  it 
forces  the  air-column  to 
assume  its  own  viljration 
rate,  unless  the  rates  of  the 
two  bodies  are  too  much  al 
\ai-iance.  In  instruments 
in  which  the  reeds  are  com- 
posed of  \er\-  dexible  ma- 
terials tlie  air-columns  im- 
po>e  their  pilches  upon  the 
reeds. 

A\  hat  has  thus  been  said 
about   orijan   ])ipes   mav  be 
ai)f)lied  with  \-arious  modifications  to  all  kinds  of  wind  instru- 
ments,  consideration   of  the  individual   peculiarities  of   which 
is   rcserx'ed    for   a    special   chapter.      The   nature 

Resonance  in  .  .  ... 

other  instru-         of  recd  actiou  in  relation  to  the  voice  is  ot  jiar- 

ments. 

ticular  miportance. 
Air-columns  mav  also  be  set  in  vil)ration  b\-  i;as-tiames. 
C'omnion  illuminatin,^^  i^as  ma\  be  used  for  this  ])ur])ose.  but 
better  results  follow  from  the  emplo_\'meiU  of 
Indrot^en.  In  Iml;'.  fu  lu'droi^'en  gas,  generated 
in  the  bottle  on  the  left,  i)asses  into  the  lul)e  in  the  rear  and 
i^  ignited  :is  it  emerges  from  a  small  opening  in  the  toj). 
When  a  glas-^  tube  of  the  ])roi)er  dimensions  is  i)laced  over 
the    tlamc     thus     ])rocluced    ;i     clear,    musical     tone     is    lieard 


66. 


Singin 
flames. 


SOLWD.  AM)  ITS  KliL.lTIOX   10  MUSIC 


^) 


l'"araday   (179l-lS()7)   (icmonstraled  that 

the    gas-flame    when    soundin.i;'    emits    a 

>eries  of  explosions  e(|nal  in   nunrner  to 

tlie   \ihration    rale   of   the   air-eolumn   in 

the    tul)e.    which    con>e(jnentl\-    resounds 

to   these   impulses.      Heside   their    funda- 

nieiUals.  such  tubes  ma_\'  i^i\'e  out  se\'eral 

up[)er  partials  when  excited  1)\-  the  flame. 

A   nuich  stronger   fundamental   tone  and 

a  greater  number  of  U})])er  partials  ma\' 

be    obtained     from     large    cojjper    tul)e^ 

under    the    influence    of    singing    flame.s 

Kastner   (1S.^2-1SS2)   constructed  a  kind 

')f  pipe  organ  in  which,  when  a  ke\-  was  ^'"-  ^^■ 

depressed,   two   >mall   flames   were  Ijrought  together  in   a  pipe 

sm  that  a  tone   was   produced.      The  dex'icc.   however.   ])roved 

more  curiou>   than   of   practical   value. 

T}  ndall   and    several   others   investigated   the   i)henomena   of 
-ensitive  flame>.      A   comiuon   "bat-wing""  burner    „ 

'^  Sensitive 

wheti  under  ordinar}-  ])ressure  as>umes  the  form    flakes. 

at   the   left   of    I'ig.   AS.   and   is   imaffected   bv    -ounds.      When 


Fig.    68. 


80 


SOL'XIJ.  .1X1)  ITS  KliL.lTlOX   lU  MUSIC 


the  gas  pressure  is  pushed  heyond  a  certain  |)oint  thx  tlame 
"flares"  in  the  manner  depicted  in  the  riglit-lianrl  drawing. 
If  now  the  gas  l^e  regulated  so  that  the  tlame  i>  just  on  the 
point  of  flaring,  the  latter  Ijecomes  >ensiti\'e  to  certain  >t.)tmi'ls. 
and  darts  out  into  a  forked  ai)i)earance  whene\'er  these  are 
produced.  This  flaring  n(jrmall\-  arises  fr(jm  a  certain  aiu(»unt 
of  friction  generated  Ijy  the  rush  of  gas  from  the  l)urner;  and 
when  the  force  of  the  gas  has  ncarK  reached  this  ])oint  the 
agitation  of  the  flame  ])roduced  hv  its  xibrations  in  s_\-mpath\- 
with  a  sound  is  sufficient  to  cause  it  to  lo--e  its  ecitiilibrium. 

1')}-  exi)erimenting  with  different  burners  .-scientists  have 
succeeded  in  producing  flames  of  a  high  degree  of  -ensitivit}'. 
T,,      ,    ,.,  Wdiat    is    called    a    steatite    burner 

The  steatite 

burner.  gi\-es.    uuder   nonual    conditions,    a 

delicate  flame  aljotit  twcnt\-  inches  long,  of  the 
form  on  the  left  in  h'ig.  (.\).  Influenced  b>' 
different  sounds  this  flame  a>sumes  wirious  other 
sizes  and  >hapes.  .^uch  as  the  one  on  the  right 
in  I'ig.  60.  High  ujjper  ])artials.  like  tho<e  pres- 
ent in  the  \-owels  /'  or  c.  cause  special  agitation. 
\A'hen  separated  from  its  burner  by  a  wire  gauze 
the  flame  becomes  so  sen>itive  that  it  respond> 
even  to  sotm(l>  inaudible  to  the  ear. 

I'hat   it   is   not   the   flame   itself    which    is   thu- 

sensitix'e  to  sottnds  but  the  gas  as  it  escapes  from 

the    burner,    has    been    pro\-ed    b\" 

Effect  of  sound  ,        ,         .  .  ,  .        .      ', 

on  unignited  -ubstitutuig  lor  tlu'  tiamc  um^nUcd 

gas, 

gas   charged    with    -luoke.      Sha])e> 
similar  to  those  assumed  b\-  the  flame  are  formed 


Ijv    such    gases    when    res])ond'ng    to    a    iuu>ical 
tone. 

.\s  nflght  be  expected  from  tlie  ex])eriment< 
with  i)enduUnus  of  uneqtial  length  recorded  on 
„„  pa'a-  ro.  a  tone  is  able  to  influence 

trtect  o.  reson-        '      '^ 

ance  on  bodies       ^q^   Qj^jy   bodics   Vibrating   to   the 

of   multiple  -^  ^ 

vibration  rates,      same  pitch  but  also  those  having 


SOUXD.  .'IND  ITS  RF.L.ITIOX  TO  MCSJC  HI 

the  relation  of  the  simple  harmonic  upper  partials  to  the 
sounding  body.  'Jhiis  a  tunini^-fork  ma\-  induce  resonance 
in  a  jar  whose  vibration  rate  is  twice,  tlirice,  or  four  times 
ils  own.  Jf  a  lone  l)e  sung  when  the  dampers  are  lifted 
fre)m  ihe  strings  of  a  piano,  not  only  will  the  siring  wliich 
gives  the  same  note  resound,  but  also  a  number  of  tones  re])re- 
senting  higher  partials  will  be  clearly  heard.     Press  down  the 

keys  representing  the  chord  c'  c'  g'  ^S=-^e^  on  the  piano  and 

slrike  c  '^=^isrz^    shar])ly,   releasing  it  immedialeK'  afterward. 

The  group  of  upper  strings  will  be  set  inlo  vibration  induced 
partly  by  the  fundamental  of  c  and  partly  by  ils  upper 
l)ariials. 

Likewise  tones  coincident  with  the  upper  partials  of 
another    tone    may    cause    these    to    sound.      1  Icjlding    down 

c  ^9^^^^^T^^      on    the    piano,    ])hi)-    and    release    a   number   of    tlie 

ui)q)cr  f's.  /:"'s  and  G's.     Many  of  these  will  now    "dSced^by"''*'' 
be  heard  vibrating  as  partials  of  the  original  c.    resonance. 
To  prove  this  fact  let  go  of  the  kev  v^diich  is  Ijcing  held  down, 
when  bv  the  consequent  fall  of  its  dam])er  the  sounds  will  im- 
mediatelv  cease. 

Certain  substances  have  so  complicated  a  structure  that 
they  are  a})i)arently  capable  of  reinforcing  any  sound  what- 
ever.    One  of  these  is  wood.     IMace  the  end  of    „,     , 

Wood   as   a 

a  sounding  tuning-fork  against  the  top  of  a  resonator, 
wooden  table,  and  a  great  increase  in  its  tone  will  result. 
whatc\-er  be  its  rate  of  vibration.  So  also  the  tones  of  a  mtisic 
box,  when  the  latter  is  brought  inlo  contact  with  a  wooden 
surface,  are  nmch  reinforced.  In  ihe  case  of  the  resonating 
box  above  alluded  to  (page  "/}>')  the  tone  of  the  tuniir-'-fork 
is  intensified  not  onK-  bv  the  air-column  in  the  box  but  also 
by  the  wood  of  which  the  latter  is  made. 

W'ithout    reinforcement    the    tone    of    a    string    is    so    slight 


82  50 cay;,  .IXf)  ITS  RliLATIOX  TO  MUSIC 

as   to   I;c   scarcely   perceptible.      This    fact   can   be   proved   Ijy 

stretching-   a    strinj/,    sus])en(le(l    in    free    air,    bv    „       ,■ 

o  o'         1  .     Sounding- 

means  of  an  attached  weight.     When  the  string   boards. 

is  vibrated  b_\-  a  \'iolin  bow  little  or  no  .sound  is  heard:  but  if 

it  be  subjected  to  an  e(|ual  tension  when  stretched  o\er  a  boartl 

a    tone    of    considerable    ^■olume    results    when    the    string    is 

sounded.      'rhu>   the    full    and    rich    tones   j^roceeding    from    a 

piano   come   in    realit_\-    from    the   \-ibrations   o\    the    .-ounding- 

board  which  ha\c  been  .-^et  in  motion  through  s\'mpath\-  with 

the  \ibrating  >trings. 

W'c  ma}'  realize  the  agitatir>n  of    the  sounding-ljoard  in  tlie 

piano  l)\-  [)lacing  a  >mall  object  such  as  a  pencil  upon  ii.     When 

a  tone  is  produced  to  which   it   can   respond,  the 

Experiments  ....  . 

with  sounding-      ])encil     Will     jar    (h.-agiccabl\ ,     nni)elled     l)v    the 

boards.  .■,..'..         '  ^       .    '     ... 

l)oard  with  which  it  is  m  contact.  A  tamihar 
children's  tov  was  at  one  time  maue  in  the  form  of  small 
figures  or  "iJUiJpets""  which  when  set  U])on  the  >ounding- 
i)oard  waltzed  about  merril\.  and  which  could  ea-ily  l)e  o\er- 
tlirown   b\'  an   especialK-  hea\\-   lone. 

All    f(jrms   of    stringed    instruments    recjuire    such    reinforce- 
ment.     Ihose  of  the  violin  t}])e  reinforce  the  string  tone  both 

b\-  their  wooden   bodies  and   aI<o   b\-  the  air  en- 
Resonance  in  :,.,.,  ,       ,  ■       ,       ,       . 
stringed                clo>ed   witliui    tlicm.      ill   tlic   casc   of    the    ijanio, 

instruments.  ,•  ,  ,      •  i  ,      i  i"      . 

the  soimding-board  is  re])laced  i)\-  a  >tretched 
membrane  like  a  drum-head  which  .also  i>  ca])able  of  re-onat- 
ing  to  anv  tone,  ])roducing.  liowxwer.  a  resulting  sound  ol  a 
duller,  le>-  elastic  qualit}-. 

Membrane.-,   on   .account  of   their  extreme   >en.-iLi\"it\    to   all 

.-ouikIs.    have    been    m.ade    the    bases    of    important    ai)i)liances 

for    recorclimj-   .and    reijroducing    sound.      An    in- 

Uses  of  ' 

n^embranes.  staiicc  of   .-uch   use  is   fouud   ill   tlic  drum.-kiii  of 

the  e.ar.  which  coiucws  exterior  <ounds  to  the  org.ans  within 
(page  10'^).  In  the  Huuioiirapli  and  the  hlcplioiic.  membranes 
h.a\e  .a  similar  function  to  pertorm. 

The  i)rinci])lc  upon  wh-ich  the  ])honogra])h  works  w.a-  known 
fur  xotne  time  before  the  imeiition  of  the  i)resenl   insirunient. 


SOlWn.  .IXL)  ITS  RliLATlOK  TO  Ml'SIC 


83 


and    was    eniploved    in    an    exiJcrinicnlal    device    „,       , 

1        -  '  1  he  pnon- 

called  the  phonaiitoijral'h.     The  latter  consisted    a^'t°g'-ap'i- 
of  a  lart^e  fuimel  which  focused  soimds  directed  into  it  u])on 
a  membrane   at   the  end.      To  this  nieml)rane   was   attached   a 
stvle    which     recorded    the    vibrations    in    zi<^za,i4'    line>    u])on 
smoked  paper  covering  a  revolving  cylinder. 

Most  of  these  features  were  retained  in  the  phoiioyrapli 
invented  by  ITlison  in  1877,  but  in  the  latter  instrument  the 
style  made  indentations  in  a  piece  of  tinfcjil  at 
var\ing  depths,  so  that,  when  the  st}'le  was 
placed  back  at  the  beginning  of  these  indentations  and  caused 
to  retrace  them  at  the  same  rate  as  at  first,  l)oth  the  style 
and  the  membrane  a])proximately  repeated  their  former  mo- 
tions, and  hence  gave  out  sounds  similar  to  the  original  ones. 


The  phonograph. 


mmmmr\ 


70.    ( )ri.t;inal  of  the  Phonoi^raph. 


The  nature  of  this  historic  instrument  ma\-  be  better  under- 
stood bv  consulting  Mgures  70  and  71,  which  give  a  general 
and  sectional  \-iew  of  its  original  fi)rm.  Soimds  trax'cl  down 
the  fimnel  P  P  through  the  mouth])iece  proper  in  in   focusing 


84 


SOl-M).  .1X1)  ITS  NJiL.rnoX   TO  Ml'SIC 


oil  ihc  nicniljranc  or  diaphragin  ;;  ii  fixed  in  the  bar  / 
wliich  is  ])i\-()te(-l  at  o  and  adjusted  by  the  >cre\v  c  at  the  to]). 
Attached    to   the    (haphragni    is    a    small    plate,    which    carries 


Fig.    71. 

the  style  p.  Thi=  style  is  not  directly  in  contact  with  the  tinfoil 
but  i)resses  on  a  sprini^-  bearing-  a  small  rounded  metal  point 
7  which  indents  the  tinfoil  .r  on  the  revolving  cylinder  JV.  As 
this  original  machine  was  \vorked  by  hand,  diffictilt\-  was  ex- 
perienced in  producing  absolute  regularitv  in  the  motions,  a 
defect  \\hich  is  remedied  in  the  modern  machines  bv  the  use 
of  a  mechanical  motor.  \'arious  forms  of  the  i)honograph 
are  now  on  the  lUcirkct,  in  which  the  records  are  made  in  a 
wax  com])ositi()n  from  which  thev  are  afterwards  reproduced 
in  firmer  materials,  .^ome  machines  still  emi)lo\-  the  cylinder 
form  of  records,  while  in  others,  sometimes  termed  gramo- 
phones, the  vibrations  are  recorded  upon  a  revolving  liorizontal 


SOUND.  JXI)  ITS  RliLATIOX  TO  MUSIC  85 

disk  in  spiral  cur\cs  wIiIcIt  proceed  from  llie  outer  edge  toward 
the  centre. 

The  implement  now  used  lor  cutting  the  record  is  different 
from  that  which  reproduces  it.  the  former  consisting  of  a 
sapphire  point  and  the  latter  of  a  similar  point  or  How  the  tone 
a  needle  of  metal  or  hhre.  One  of  the  greatest  is  reproduced, 
marvels  of  science  is  illustrated  in  the  comhined  work  of  these 
little  tools,  the  hrst  of  which  ploughs  into  the  wax  a  reproduc- 
tion of  not  only  a  single  sound  with  its  attendant  overtones, 
but  frec|uentl\-  of  manv  other  accompanying  sounds,  each  with 
its  characteristic  quality,  and  the  second  of  which  travels  over 
each  minute  indentation  with  fulelit}',  transmitting  its  complex 
motion  to  the  diaphragm,  whence  it  is  conveyed  through  the  air 
to  the  ear  of  the  listener.  If  we  could  trace  out  one  of  the 
grooves  in  this  record  with  a  microscope,  its  appearance  would 
be  found  to  resemble  that  presented  by  the  ruffled  surface  of  a 
lake  seen  through  a  slit  in  a  card.  Long  indentations  made 
by  the  fundamental  tones  would  be  seen  traversed  by  number- 
less ripples,  each  corresponding  to  an  overtone  or  another 
fundamental,  and  each  having  a  dei)th  proportional  to  its 
intensity. 

Several  instruments  have  been  devised  to  bring  ])honograph 
indentations  into  readable  form.  Professor  McKendrick.  of 
Glasgow,   constructed   a   "phonograph    recorder"    Experiments 

r  1  1  r  1    •    1       1  11  •        '^'*'^  phono- 

irom  the   results  oi   which  he  was  able  to  csti-    graphs. 
mate    the    enormous   number   of    x'ibrations    involved    in    even 
quite  simple  sounds.     In  the  record  of  the  words  77/r  Royal 
Society  of  Eilinburgh,  for  instance,  he  discovered  over  30()0 


Fig.   72.   Curve  of  the  pronoun  A 


86  SOUXD.  AXD  ITS  REL.ITIOX   Tu  ML  SIC 

\ibrations.  Vxg.  72  shows  a  graphic  record  of  the  sound 
of  the  vowel  /,  made  by  lulward  S.  W  lieeler,  of  ^'ale  Uni- 
versity, as  the  resuh  of  similar  ex])eriments.  The  possibili- 
ties of  stich  devices  in  determining  the  composition  of  tone> 
can   readily   l)e   recognized. 

The  tclcpJiDiic  also  depends   for  its  action  up<jn  the  \ibra- 

tions    of    ;i    menil)rane    which    catche>    the    sounrls    impinging 

u])()n    it.       In    the    traiisDuttcr    these    vil)rations 

The  telephone.  i  j  •  •  i  •  i    •     i 

])rt)duce  tiuctttations  m  an  electric  current  which 
carries  them  through  a  wire  circuit  tn  any  doired  jilace. 
There  they  in  turn  affect  the  membrane  of  the  rccci\-cr.  wliich 
reproduces  them  to  the  ear  of  the  li-tener.  [lU'enied  b\-  ( Jra- 
hani  ]lell  in  IS"''),  the  tele])hone  was  at  fir-t  of  no  commercial 
\alue  (in  acccnmt  of  the  indistinctness  of  the  rejjrorluctions. 
lly  means  of  inan\-  cle\'er  devices  which  have  enonnousK-  in- 
crea-^efl  its  sen-itivity.  however,  it  has  now  attained  ilie  ])0>i- 
tion  of  a  household  neces>it}".  .\t  lir>l  n>  <  di-tinctiiin  was 
made  between  the  transmitter  and  tlie  receiver.  W'liile  tlie 
latter  has  retained  mucli  o\  its  original  form,  the  tran-^mitter 
is  now  fjuite  dift'erent.  its  ethcac\-  having  lieen  greatl\-  aug- 
mented b\-  the  tise  of  carl)on.  Animal  memiirane^  ha\c  lieen 
generallv  re])Iaced  in  br)th  ])lK;nograph  and,  telephone  b\-  thin 
di>ks  of  mica  or  metal. 

l'erha])s  the  mo>t  remarkable  manifestation-  of  the  ])he- 
nonicna  of  roonance.  howe\'er,  are  found  in  connection  with 
o  .  ihe  human    \"oice.      \\\   directing  the   air   current 

Kesonance   in  ■ 

the  voice.  j,-,^^,  ^\^^  cavities  of  the  head,  mouth   and  ihri-at. 

and  b\-  miidifving  the  sha])e  of  the-e  ca\'itie-.  the  -])eaker  or 
-inger  is  able  to  ])roduce  an  infinite  numljer  (>f  moditicatii  ais 
in  tonal  intensit\-  anrl  nualitw  l-"urther  ci 'ii-ideralioii  > .{  ihi- 
important  phase  of  resonance  i-  re^-erxed  f(jr  Chapter  \  III. 


SOUND,  AND  ITS  RELATION  TO  MUSIC  87 

SU\mARY. 

Resoxanci:,  or  sympathetic  vibration,  depends  upon  tlie 
principle  that  a  nimiber  of  shght  iniptilses  properly  applied  will 
linally  create  considerable  momentum. 

A  very  rigid  body,  to  be  aftectcd  by  the  sound  coming  from 
another  bod\',  must  be  either  in  perfect  unison  with  this  sc^mul 
or  must  have  a  vibration  rate  which  is  a  simple  multiple  of  that 
of  the  sounding  body.  J^)odies  of  less  rigidity  mav  respond 
when  they  are  not  absolutely  in  unison  with  the  sound  which 
strikes  them. 

Instruments  called  resonators  are  capable  of  selecting  out 
special  sounds  for  reinforcement,  and  may  even  develop  sounds 
ordinariK-  imperce])til)le  to  the  ear. 

Air-columns  in  tubes  can  be  made  to  resound  under  the 
influence  of  ttining-forks,  the  ""whistle"  device,  reeds,  and  gas- 
flames. 

Reeds  in  organ  pipes  are  either  striking  or  free. 

Sensiti\-e  flames  are  of  value  for  testing  the  properties  of 
sounds. 

Sounding-boards  and  membranes  are  apparently  capable  of 
responding  to  an\  sound  whatever.  The  former  are  usefttl  in 
reinforcing  the  tones  of  strings,  especially  those  of  the  piano 
and  of  the  \-iolin  family.  Membranes  are  chiefly  employed  for 
recording   and   reproducing  sound. 

REFEREX'CE  LIST. 

HchiilioUz.  Chapter  3. 

Barton.  Cliaplcr  (i. 

Zaiini.  Chapters  (\  7. 

I'yiidall.  Cliapters  3,  5,  6. 

Harris.  Chapters  7,  10. 

Broadhousc.  Chapters  6,   10. 

Poynt'nig  and  Tlu>}}ipson.  Chapters  4,  7,  8,  9. 

Stoiic.  Cha])ter  3, 

Taylor.  Chapter  3. 

Ba>'uc.':.  Cliapters  4.  7,  8. 


SOUND,  AND  ITS  RELATION  TO  MUSIC 


La^ngnac,  Chapter  1. 
Catchpool,  Chapter  5. 
Blascrna,  Chapter  3o 


CHAPTER  VII, 

ScALi':s.  L\ti-:k\ ALs  and  Chords. 

Having  reviewed  the  chief  facts  i)ertaining  to  the  nature  an<i 
properties  of  sound,  we  will  now  inquire  how  certain  sounds 
ha\e   been    selected    and    s\-steniatized    from    the   ^  .  .      , 

Urigin    or 

well-nigh  limitless  number  at  our  disposal.  In  scales. 
all  jn-obability.  attempts  at  music  in  the  form  of  vocal  utler- 
arce  were  coeval  with  speech  itself;  indeed,  manv  scholars 
contend  that  song  antedated  the  spoken  word.  Certainly  at  a 
ver\'  earl\-  period  in  the  history  of  primitive  peoples  mere 
insensate  bowlings  must  ha\'e  given  place  to  sounds  of  a 
more  stable  nature.  When  tones  of  varying  pitches  thus  came 
to  be  em])loyed  in  melodic  progressions,  thev  naturally  ranged 
themsehes  in  a  graded  series,  each  luember  of  which  was  fixed 
in  its  relati(3n  to  the  others.  X'arietv  was  also  insured  in  this 
series  or  sca'e  (Catin  scala,  a  ladder)  by  the  presence  of  inter- 
wals  of  different  dimensions. 

In  using  the  word  ijitcrz'cil  in  music  we  should  bear  in 
nnnd  that  in  defining  it  as  tlic  difference  in  pitch  hetiveen  two 
tones  we   refer  not  to  the   numerical   dift'erence 

.....  Definition  of 

])etween    then-    vibration    numbers,    but    to    the   the  word 

,  ,  ,  ...       "interval." 

proportion  existing  iietueen  these  niunbers.  which 
remains  constant  for  any  given  interval.  Thus  the  upper 
tone  of  an  octave,  vibrating  twice  as  fast  as  the  lower, 
is  related  to  it  as  two  is  to  one;  a  proportion  re])resente(l 
by  the  fraction  -/^.  Tf  the  lower  tone  vibrates  100  time- 
per  second,  the  tii)pcr  must  vil)rate  ^/^  x  100  or  200  times 
per  second,  so  that  the  dift'erence  between  the  vibration 
numliers  will  be  100;  but  if  the  lower  tone  vibrates  200  times 
per  second  the  u])per  must  vibrate  -/^  x  200,  or  400  times,  with 
a  conseciuent  rate  diii'erence  of  200.  In  both  cases,  of  course, 
the  interval  is  the  same. 

Such  a  >election  of  tones  as  has  been  described  is  in  many 


90  SOUND,  AND  ITS  RELATION  TO  MVSIC 

respects  a  purely  arbitrary  one,  resulting  in  the  formation  of 
„  diverse  scales  among  distinct  nationalities.    Xcv- 

Common   use  " 

of  the  octave.  erthclcss  there  are  a  few  intervals  which  are 
common  to  nearly  all  musical  s}'stems.  \\  hen,  for  instance, 
men  and  women  attempt  to  sing  the  same  tune,  it  is  natural 
for  them  to  pitch  their  voices  an  octave  apart ;  and  so  intimate 
is  the  relation  between  these  octave  tones  that  the  partici- 
])ants  often  believe  that  thev  are  singing  in  unison.  For  the 
same  reason  we  speak  of  a  tone  as  repeated  in  another  octave 
when  the  two  tones  are  an  octa\'e  or  a  multiple  of  an  octave 
apart.  Hence  the  characteristics  of  any  scale  are  alwaxs  in- 
cluded within  the  compass  of  an  octave,  while  anv  extensions 
of  the  scale  will  arise  from  the  repetition  of  the  same  inter- 
vals in  succeeding  octaves. 

The  xeJiolc  tone  or  whole  step,  a])proximatelv  one-sixth  of 
an  octave,  is  the  general  unit  of  measurement.  (Jther  inter- 
^^.       .  ^       ,       \als   freciuentlv    found  are   the   i)erfect   fifth   and 

Other    intervals  '  -  ' 

in  frequent  use.  perfect  fourth.  represented  in  our  scale  by  C-G 
and  C-l\  and  measuring  rcspectix'elv  3'j  and  2'j  stcjjs.  F,x- 
cei)t  in  the  case  of  the  inler\'als  cited,  hovv'ever,  there  is  little 
uniformit}'  in  dillerent  systems. 

We  mav  in  general  distinguish  two  classes  of  scales,  the 
first  of  which  avoids  intervals  smaller  than  a  whole  ste]). 
„         ,  while  the  other  .'-ubdivides  the  >tei)  into  interx'al-^ 

1  wo    classes  ' 

of  scales.  which    are   sometimes   exceedingl\    minute,      'flic 

chief    scale   of   the    first    class    is    the   peiitatoiiie    or    five-note 
-cale,    which    embraces    three    u-hole-slep    inter\-als    and    two 
interw'ds  of  a  -lep  and  a  half  each,  tluir- :     ^ 
(  Figures  beiieatli  refer  to  >te])s  and  frac-   /r,  ^^  \,  _o-  "-  *-    -^ 
tions  of  ste])s.  )     Its  effect  ma_\- be  judged  '     '    '-    '     "- 

,  ,     .        1)\-   ])la\in"-   in    >uccL-->ion   the   1,'lack   ke\s   of    the 

1  he  pentatonic  .      i       .        .^  • 

^"'<^-  i)ianofnrtc.      ( 'liine-c    folk    tunes   are    almo-t    in- 

\arial)l\-  t'ounded  u])on  thi<  scale,  wliich  is  re\ered  a-  the 
>u])ernaturall_\-sent  foundation  of  mu.-^ic :  and  although  in 
China  twc-Ke  dix'isions  of  the  octax'e  are  recognized  in  tlieorx', 
the  ])cnt.atonic  --rale  -till  retains  its  i)re-tige  in  i)ra'-tical  u-ai;c. 


SOUND.  AND  ITS  RELATION  TO  MUSIC  91 

Japan  and  other  Oriental  nations  employ  a  similar  scale,  while 
its  existence  in  Scotland  is  plainly  evidenced  in  popular  melo- 
dies. 

In  our  own  system  the  octave  is  di\ided  by  semitones  or  half 
steps  into  twelve  parts;  and  from  a  combination  of  live  whole 
steps  and  two  half  stei)s  the  major  eight-tone  di- 

/■  Use  of  the 

atonic  scale  ^'  ^"..   »  "t7"^E^^  is  formed,   ^^^^  ^"p- 

which  is  the  basis  of  our  music.  Our  harmonic  minor  scale 
eni])loys  the  interval  of  IVz  steps  between  the  sixth  and  seventh 

decrees,    thus :  -Vh  ~i       TT^"^'^"^^   In    some    scales    still 

t;reater  variety  is  secured  by  again  inserting  this  interval  be- 
tween successive  degrees  of  the  eight-tone  scale. 

Among  stronglv  imaginative  j^eoples  there  is  a  tendency 
toward  the  use  of  minute  intervals.  The  ancient  Hindoos,  for 
instance,  divided  the  octave  into  twenty-two  ^^^^^^  ^jj^ 
])arts,  and  the  Arabs  into  seventeen,  the  latter  minute  intervals, 
determined  in  accordance  with  mathematical  princii)les.  A 
multi])licit\-  of  scales  is  the  general  secjuence  to  so  ct)mplicated 
a  system  of  subdivision. 

Intervals  as  small  as  the  (|uarler-step  also  existed  in  the 
scales  of  the  ancient  (ireeks.  h^our  tones  arranged  within  the 
compass  of  a  ])erfect  fourth,  seems  to  have  con- 

•  I  1      1  1-  ,  •         1  1  -n   ■  ■         1     '^'^'^  foundation 

stituted  the  earnest  ( ireek  scale.  I  his  received  of  the  Greek 
the  name  of  tctrachord.  or  scale  of  four  strings, 
from  the  fact  that  its  tones  corresponded  t(^  the  tuning  of 
the  four  strings  of  the  original  lyre.  Terpander  the  Spartan, 
in  the  se\enth  centur\'  \\.  C.  combined  two  tetrachords  bv  a 
common  note,  producing  a  scale  which  had  the  com]:)ass  of  a 
seventh;  and  Pythagoras  (died  about  500  R.  C.)  increased 
this  to  an  octave  by  placing  a  step  between  the  two  tetra- 
chords. 

The  latter  philoso]:)her  investigated  the  vibrations  of  strings 


9Z  SOCXD,  AND  ITS  RELATION  TO  MUSIC 

by  means  of  the  inonoclwrd,  a  i)riniitive  form  of  the  sonom- 
Theoryof  ^^^^   i^'^S-  -- ) ■     -I"  ^^^^^  ^vav  he  discovefed  that 

Pythagoras.  when   the   length   (jf   a   stretched    string   was   di- 

vided in  the  proportion  of  two  to  one,  the  interval  produced 
by  soiniding  the  two  segments  together  was  an  octave;  that  a 
di\"ision  of  three  to  one  resulted  in  a  ])erfect  fifth;  and  that 
one  of  four  to  three  gave  a  perfect  fourth.  lM"om  these  re- 
sults he  deduced  the  ])rinciple  that  "the  simpler  the  ratio  of 
the  two  parts  into  which  the  vibrating  string  is  divided, 
the  more  perfect  is  the  consonance  of  the  two  sounds,"  a 
theory  of  which  llelmholtz  was  the  first  to  gi\c  a  logical 
exi)lanation. 

J'Mhagoras  constructed  an  eight-note  scale  by  starting  with 
an  octave  and  inserting  the  inter\'ening  tones  found  b\-  pro- 
The  Pythagorean  '-Ceding  by  i)erfect  hfths  from  the  lower  tone; 
^'^^''^-  thu<  beginning  with  the  octave  C'-C  he  went  from 

the  lower  C^  by  fifths  to  (/,  D,  .1.  IL  and  B.  lowering  the  tones 
outside  the  original  octave  to  their  position  within  it  b_\'  octaves, 
and  adding  I' .   a  perfect   fotirth   abo\c   ( '. 

Two  results  of  this  process  should  be  noted.  It  was  dis- 
ci:)\'ered  that  the  third  tone  /:  was  related  to  ('  in  the  compli- 
o     ,,      ,  cated    ratio   of    -fV,    and    hence    the    major    third 

Results    of  tj  -» ' 

this  scale.  .^^.^^  cla>sed  as  a  discord,     'fhen  also  P_\thagoras 

found  that  if  he  extended  his  circle  of  fifths  as  follows: 

r,  G.  D.  ./,  R,  B.  Ft.  Ct.  Ct.  m..\t.  /!:,  Bt, 
the  final   Bt   w;is  shar])er    by  about     -W    than  the  nearest  C. 
obtained  bv  raising  the  (original  ('  bv  ()Cla\'es.  and  that  when 
he  ])roceeded  downward  by  fifths  as  follows- 

C,  /•.  Ih.  Eh,  .lb,  nb,  Cfb,  Co,  l-b.    Boo.  Ebb,  Abb,  /)-b. 
the    final    /'bi    was    flatter    than    its    nearest    ("    b_\-    the    -amc 
amount,      'fliis   discrepancy  ha>   been   called   the   Pythaf/orcan 
c  omnia. 

With  the  tetrachord  as  basis  the   Cireek^   formulated   three 
classes  of   scales  or  modes,    'fhe   first   or  diatonic  genus  em- 
braced  all   possible   arrangements   of   whole   and 

Greek  modes.  ,      ,  -  ....  '  .  ^  ,  , 

halt    ste]:)s  within  tlie  com])ass  ot   a   tonrth  ;  the 


SOUND,  AND  ITS  RELATION  TO  MUSIC 


93 


second  or  chromatic  genus  combined  two  half  steps  witli  tlie 
interval  of  a  step  and  a  half  ;  while  the  third  or  enharmonic 
genus  embraced  two  quarter  steps  and  an  interval  of  two  whole 
steps. 

The  following  illustrations  of  (Ireek  modes  in  modern  nota- 
tion do  not  rej)resent  their  absolute  pitches,  which  varied  some- 
what. Scales  were  conceived  by  the  Cireeks,  in  common  with 
most  early  peoples,  as  proceeding  downwards  instead  of  up- 
wards as  in  our  musical  system. 

Examples  of  the  three  genera : 


Dialdiiic 


Enharmonic 


Most  important  of  these  genera  was  the  diatonic,  of  which 
seven  modes  were  recognized.  Jn  each  of  these  the  octave 
compass   was   completed    bv    joining   two   tetra- 

'  -        ,,        .  Diatonic  genus 

chords   together ;    and   all   became   hnally   mcor-   and  complete 

system. 

porated  mto  a  so-called  "complete  system,     two 
octaves  in  length,  to  each  note  of  which  a  name  was  given, 
taken  from  the  nomenclature  of  the  lyre  strings.     The  result 
was  as  follows ; 


Hypo -Dorian 

Hypo-Phrygian 
Hypo-Lydian 


\        \        \        \  Dorian                   i        i  i        : 

Phrygian  : 

I         i                    Lydian  ; 

I Mixo  Lydian  '         | 

The  complete  Greek  system. 

Undoubtedly  Greek  music  played  an  important  part  in 
forming  the  music  of  the  early  Christian  church.  The  latter, 
at  first  purelv  vocal,  consisted  of  unison  melodies.    „ 

^  '  Gregorian 

generally  not  more  than  an  octave  in  compass  and    "^odes. 

based  upon  scales  that  were  not  definitelv  formulated  for  some 


94 


SOUND,  AND  ITS  RELATION  TO  MUSIC 


time.  Ultimately,  however,  these  scales  were  arranged  in  a 
series  of  "chtirch"  or  "Gregorian  modes"  supposedly  the  same 
as  those  of  the  ( ireck  diatonic  genus,  h'our  authentic  modes 
were  sup])lemente(l  by  an  equal  number  f)f  plagal  modes,  each 
of  which  was  a  fourth  lower  than  its  corresponding  authentic. 
Later  on  four  others  were  added.  Lach  mode  had  two 
notes  of  s])ecial  importance,  the  linal  or  ending  note  and  the 
doiuinant  or  reciting  note,  which  are  shown  in  the  table  of  the 
orii/inal  modes  formulated  in   Iwg.  72>. 


Finals       Dominants 


Fig.    73. 

The  numbers  before  the  scales  indicate  the  following  modes: 
Authentic.  Plagal. 

I.   Dorian.  II.    Hypo-Dorian. 

111.    Phrygian.  I\'.    1  lypo-1'hrygian. 

\'.    L\(lian.  \'I.    1  ly])o-I,ydian. 

\I1.   Mixo-l.\(lian.  VIII.    1  lv])<,-.Mixo-Dydian. 

i  lalf  stejjs  arc  shown  by  slurs.  olbcrwi,-,c  whole  -leps  prevail, 
r.v  the  eleventh  centurv  all  these  scales  were  united  in  a  long 


SOUND,  AND  ITS  RELATION  TO  MUSIC  95 

scale  of  about  two  and  a  half  octaves,  extending  from  G  to  c" , 
and  divided  into  seven  overlapping  scales  of  six  notes  each, 
called  lie.vachords. 

Meanwhile  the  dance  rhythms  and  secular  songs  of  the 
l)eople  were  conforming  to  scales  which  were  able  to  give  a  de- 
siraJjle    sense    of    linalitv    to    the    verse    endings 

■  Rise  of  major 

oi    rlumed   stanzas  oi   poetry.      .V  tune   and   its   and  minor 

,  .  ^  ,  scales. 

accompanying  harmonies   were  made  to  revolve 
around  a  central  tone,  to  which  an  ending  formula  or  cadence 
hnally  led.     Thus  tonality  was  evolved  ;  and  with  it  came  the 
dominance   of    the    so-called    major   and    minor   scales    which 
eventually  superseded  the  older  forms. 

.  This  change  in  attitude,  together  with  the  growing  complex- 
ity of  music  due  to  the  [)Oi)ularity  of  instruments  and  the  con- 
seciuent  rise  of  new    forms,   presented  problems    „     ,,. 

^  '11  Resulting 

to   the   theorists   of    the   later   fifteenth    and   the    p^-obiems. 
sixteenth   centuries   which   provoked   much   controversy,      Let 
us   see   what   these   problems    were,   and   how   they    were   dis- 
posed of. 

Jt  was  tirst  necessary  to  establish  the  proportion  of  the 
intervals  of  the  major  diatonic  scale  of  eight  notes,  which 
came  to  be  regarded  as  the  basis  of  our  musi-    ,      .•        r 

"^  Location    of 

cal  s\  stem.     This  proportion  was  determined  by   diatonic  tones, 
adopting  the  relations  discovered  in  the  hrst  fifteen  harmonic 
I)artials  resulting  from  the  equal   subdivisions  of  a  vibrating 
string,   as   shown  in  Fig.   74.     From   this   series  we  perceive 


Pit  octave 


74. 


that  the  interval  of  a  whole  stc]),  first  required  for  constructing 
the  scale,  occurs  ])etwcen  c"  and  d" .  the  eighth  and  ninth  par- 
tials.       According    to    the    laws    of    strings    c"    must     vibrate 


96  SOUXD,  AND  ITS  RELATIOX  TO  MUSIC 

eight  times  while  d"  vibrates  nine  times ;  or,  in  other  words, 
their  ratio  of  vibration  is  9  to  8,  represented  by  the  fraction 
-|.  This  interval  of  a  whole  step  is  called  a  major  second. 
Hetween  c'  and  c'  is  the  interval  of  two  whole  tones,  called  a 
major  third;  and  for  reasons  similar  to  those  just  advanced  the 
ratio  may  be  represented  by  the  fraction  ^.  From  g  to  c, 
a  perfect  fourth,  we  derive  the  fraction  |-  ;  from  g  to  c\  a 
major  sixth,  the  fraction  -5,  and  from  c"  to  b" ,  a  major  sev- 
enth, the  fraction  ^f-.  These  results  are  summed  up  in  Fig. 
75,  each  fraction  showing  the  relation  which  the  note  above 
it  bears  to  the  tonic  c. 


Cnison     Maj  2""    Mnj  S^.d     Per  4'h     Per5'!i    Maj  6'^    M--ij  7'h   Per 


Fig.    75. 

Other  important  intervals  in\olved  in  this  scale  and  also 
derived  from  the  partials  of  strings  are  the  minor  third  from 
~,       .  c'    to    (/'.    with    th.e    rati<)    of  ---.    and    the   minor 

The  minor  •'  o  ■ 

third  and  sixth,     gixth,  from  c'  to  c" ,  with  the  ratio  f. 

The  scale  thus  formed  is  called  the  "true""  or  "just""  scale, 
in  distinction  from  the  "tempered"  scale  (page  103  i.  \\"e 
„,     ...    ,„  note  that  the  major  third  is  simplified  to  4  or   ,'■  4. 

The      just  -  1  4  !■  4 

^'^^'^-  against  the   Pythagorean  major  third   of  -f^.  so 

that  the  upper  tone  (jf  the  latter  is  slightly  sharper  in  pitch  than 
that  of  the  "true""  third. 

From  the  table,  V\g.  74,  we  can  also  determine  the  ratio 
b(;tween  contiguou>  >cale  notes  ])y  applying  the  mathematical 
T3    .  principle    that    the    ratio   of   the    difference    be- 

between  twccn  two  intcrvals  is  found  by  dividing  the 

contiguous  ■'  ^ 

scale-tones.  ratio  of  the  greater  by  that  of  the  less.     The 

results  are  as  follows  : 

c,    D,    /-:.    F,    r;,    .-i,    b,    c. 

V  ^  9 '        1  .'j         8  9  8  15 

A\"e  notice  that,  while  the  half   steps  have  the   same  ratio  of 


SOUND,  AND  ITS  RELATION  TO  MUSIC 


97 


yf ,  the  whole  steps  vary  in  size,  three  having  the  ratio  |  and 
two  the  ratio  ^ .  The  shght  difference  of  g^-  between  them 
is  called  a  comma. 

After  the  diatonic  scale  was  thus  formed  the  whole  steps 
were  subdivided  by  chromatic  or  "colored"'  tones,  so-called  be- 
cause  they   gave   varied    shadings    to   a   melody. 
These,    at    first    used    only    bv    singers    to    give    chromatic 

,  .  '.         '  .  ,     tones. 

smoother    voice    progressions,    were    atterward 
adopted  by  composers,  who  discovered  that  they  were  available 
not  only  for  melodic  purposes  but  also  as  a  means  of  changing 
the  tonality,  or  modulating. 

To  make  this  key-interchange  possible  the  new  tones  must 
have  the  proper  relations  to  the  other  tones  of  the  scale  in 
which  thev  occur.     Thus,  since  the  seventh  tone    ^      ^.       , 

'  Location  of 

B  of  the  scale  of  C  is  a  major  third  above  the    chromatic  tones. 

fifth  tone  G,  the  same 
relation  must  exist  be- 
tween the  fifth  and  sev- 
enth tones  of  the  next 
scale,  G ;  hence  F^  is 
placed  a  major  third 
above  D.  In  like  manner 
C5  is  placed  a  major  third 
above  A,  G<  above  E, 
Dt  above  B,  and  A* 
above  F^.  After  locating 
the  flats  by  a  similar 
process  we  shall  find  that 
corresponding  sharp  and 
flat  tones  such  as  F-  and 
Gb  are  not  exactly  in 
unison,  but  that  of  the 
two  the  flat  is  a  comma 
higher  in  pitch. 

We     have     said     that 
Fig.  76.  Holmholtz  was  the  first 


9.S  SOfXD,  AXD  ITS  RIiL.lTJOX   TO  MUSIC 

„,,,,,  to    answer    satisfactorily    the    ciuestion    of    what 

nelmnoltz  s  -  i 

*"''^"-  causes   consonance   and   (hssonance.      Vov   inves- 

yating  the  relations  between  the  tones  he  invented  the 
double  siroi  (Fig.  76),  which  is  a  comi)lex  form  of  the 
instrument  shown  in  I'ig.  19.  llelmholtz's  siren  contains 
two  disks  which  can  l)e  rotated  either  individualK-  or  in 
unison.  In  the  lower  of  these  four  sets  of  holes  number 
8,  10.  12,  and  18  respectively,  while  four  corresi)()nding  sets  in 
the  up])er  number  9,  12,  15.  and  16.  .  I  antl  B  are  ducts  through 
which  the  \\-ind  i>  introduced  bv  pressure  from  an  acoustic  bel- 
lows. Ke}'s  at  a  and  /'  serve  to  throw  into  action  an^•  desired 
series  of  holes.  At  CD  is  a  clock-work  device  used  to  record 
the  number  of  revolutions  of  the  disks,  luich  of  the  latter  i,- 
enclosed  in  a  brass  box  which  forms  a  resonator  for  certain 
tones.  In  the  illustration  a  part  of  the  lower  box  has  been 
removed  in  order  to  reveal  the  disk.  A  crank  attachment  ai 
/:  serves  lo  raise  or  lower  the  pitch  of  the  tone  gix'cn  bv  the 
upi)er  disk,  bv  rotating  in  either  direction  the  cvlinder  which 
encloses  it. 

I'>y  emplo}-ing  the   proper   combinations   of   holes   and    rota- 
ting the  disks  in  unison   I  lelmholtz   was  able   to  jiroduce   the 
different  vibration  ratios  involved  in  the  various 

Experiments  .  .  .  . 

with  this  mtervals  ot  the  scale:  thus  bv  openmg  the  series 

siren.  .       .  ,      ,  .  ,  "      ,.  ,       .     ,         . 

ot  Sixteen  holes  in  the  upper  disk  and  eight  m 
the  lower  the  resulting  ratio  of  |  gives  the  octave,  while  the 
two  series  of  eighteen  and  twelve  holes,  having  the  ratio  of 
i;-  give  the  perfect  tifth,  and  so  on.  The  most  significant  re:-ult 
of  the-e  experiments,  however,  was  in  connection  with  tlie 
>ound-interferences  which  cause  beats  (page  44).  In  the 
case  of  the  octave  and  tifth  no  beats  were  heard,  but  with  all 
the  other  intervals  beats  were  ])resent,  var_\"ing  in  rapidity 
and  intensit\-  with  the  character  of  the  inter\-al.  Generall}'. 
when  an\'  "true'"  interval  was  put  out  of  tune  1)\-  aUering  the 
])itch  of  the  upper  tone  an  acceleration  of  the  beats  followed. 

Consonance    and    dissonance,    according    to    I  lelmholtz,    are 
determined  b\-  the  nature  and  frccjuencv  of  these  beats.     As  t<i 


SOIWD.  JXD  ITS  KEL.iriOX   TO  Ml'SIC  W 

the  first  of  these  factors,  he  showed  that  Ijeats    „  „, 

Lonsonance  ana 

are   i)roducecl   not  onlv  bv   the   fundamentals  of    dissonance 

y  -         .  depenclent   on 

two  tones  l)ut  also  h}'  their  upper  partials  and  beats, 
even  their  resultant  tones  (page  47  ).  Only  the  most  prominent 
of  these  secondary  factors  are.  however,  strc^ng  enough  to  pro- 
duce beats  of  any  importance ;  and  as  their  conflicts  vary 
greatlv  in  character  there  are  wide  ditterences  in  the  relative 
intensities  of  their  beats. 

The  eiiect  of  beats  is  determined  even  more  largely  by 
their  frequencies.  \'erv  slow  beats  are  not  necessaril\-  dis- 
agreeable, but  as  thev  grow  quicker  thev  attect    „ 

&  ,      i5  1  .  frequency 

the  ear  much  as  a  flickering  light  attects  the  eye.  °^  '^^^*^- 
.After  reaching  a  maximum  of  unpleasantness,  howe\'er,  thev 
become  merged  together  like  the  spokes  of  a  revolving  wagon 
wheel.  Helmholtz  concluded  that  when  the  number  oi  beats 
given  out  1)\-  an  interval  la\-  within  the  disagreeable  zone  the 
interval  was  dissonant,  and  that  if  these  l)eats  either  increased 
or  decreased  in  number  sufficiently  the  interval  became  con- 
sonant. 

r.ecause,  however,  of  the  proportional  nature  of  interval-, 
we  might  suppose  that  a  much  wider  interx'al  in  the  lower 
part  of  the  scale  would  be  dissonant  than  in  the 

,  ,.  ,.  .  1        -1  Effect     of    beats 

upi)er  ])art,  smce  the  difference  m  actual  vibra-    in  different 

,  .      ,  .  ,        .  ,       registers. 

tion  numbers  of  the  upper  inter\-als  is  so  mucli 
greater.  'Idiis  condition  docs  in  fact  result  only  to  a  limited 
extent  since,  as  has  been  proved,  the  number  of  perceptible 
beats  is  smaller  in  tlie  lower  part  of  the  scale  than  in  the 
upi)cr.  although  not  in  proportion  to  the  increased  number 
of  vibrations  which  compose  a  given  internal.  If  we  nla}' 
major  or  minor  thirds  on  the  extreme  bass  part  of  the  piaiic^ 
and  then  in  the  treble  register  we  are  at  once  aware  of  the 
comparative  roughness  of  the  former. 

To  show  graphicallv  the  degrees  of   -moothness  or  rough- 
ness  of    the   ditterent    scale   intervals   Ilelmholtz 

Diagram  of  ,,.-..,  ,  , 

consonance  coustructed    a    diagram    similar    to    that    shown 

and    dissonance.      .  _    '"  ....  ,  , 

in     hig.     //.       Consonance     is     indicated    when 


100 


SOL'XD.  AXD  ITS  RELATIOX   TO  Ml'SJC 


Fig.    7/ 


the  wavy  line  touches  the  horizontal  line,  while  rous^hnes>  or 
dissonance  is  proportion- 
al to  the  divergence  of 
the  two  lines.  Thus  per- 
fect consonance  appears 
at  c.  f.  and  g,  slight  dis- 
sonance is  evidenced  at 
the  major  third  and 
sixth  e  and  a  ;  while  the  increasing  dissonance  reaches  a  maxi- 
mum near  either  c. 

Lissajous  (1822-1880)  invented  an  apparatus  in  which 
small  mirrors  attached  to  a  couple  of  tuning-forks  were  s(j 
„     , .    .,,  located  as  to  throw  upon  a  screen  the  combined 

Graphic  illustra-  ' 

tions  of  beats.  niotiou  of  the  forks,  with  the  result  that  curves 
were  reflected  that  were  simple  or  complex  according  as  the 
interval  between  the  forks  was  consonant  or  dissonant.     In  a 


Fig.    78. 

similar  device  invented  bv  Kocnig.  shown  in  hig.  /8.  one  of 
two  electrically-excited  forks  liears  upr)n  its  ]M-ong  a  piece  of 
smoked  glass  upon  which  a  st}"le  on  a  ])rong  of  the  other  fork 
is  made  to  trace  a  record  as  tlic  latter  fork  is  mo\'ed  along  at 
right  angles  to  the  former,  .^ome  of  the  results  witli  forks 
of  warving  fref|uencic^  are  >ho\vn  in  I'ig.  7'K  uu\<"U  forks 
giving  the  simple  curves  of  the  first  example,  the  octa\-e  next 
shown   imparting  a  twist  to  the  hgures.   which  are  much   dis- 


SOUXD,  AXD  ITS  RELATION  TO  MUSIC 


101 


turbed  as  the  octave  is  put  slightly  out  of  tune  in  the  third 
example.      The  niajor  third  and   the  half   step   shown  in   the 


^JS^^^^^^M^^^^ 


Fig.    79. 

fourth    and    fifth    cxam])les    display    the    expected    growth    in 
intricacw 

A  cliord  in  music  results  from  the  combination  of  three  or 
m(3re  tones.  Two  thirds  joined  bv  a  common  tone  make  a 
triad :  and  this  triad  is  consonant  when  not  onlv    .,  ^         . 

Nature    ot 

the  indi\-idual  thirds  are  consonant.  Init  also  the  ^'^'^'^^■ 
fifth  ])ro(luce(l  b}'  their  union.  Onlv  two  distinct  triads  of 
this  nattu"e  are  i^ossible  in  our  musical  sxstem  :  the  major,  in 
which  the  lower  third  is  major  and  the  upj)er  minor,  and  the 
viiiiur,  in  which  these  positions  of  the  thirds  are  reversed.  In 
both  cases  the  fifths  are  ])erfect.  Three  jiositions  of  each 
triad  are  recognized,  according  as  either  note  is  jjlaced  beneath 
the  others.  Since,  also,  the  triad  tones  may  be  located  in  dif- 
ferent octaves  and  mav  be  reduplicated  at  will,  there  is  much 
possible  ^•ariety  in  their  combination. 

From  a  studv  of  the  resultant  tones  Tlclmholtz  selected  six 
combinations  of  the  major  triad  as  mo-t  jierfect  and  six  as  less 


102 


SOiWD.  .IXD  ITS  RliLATIOX  TO  MUSIC 


r,     ^.     ■        r    i)erfeci.      Tlu'se  are   <li()\vn   in    Fii/s.   80  and  81. 

Combinations  or      '  ' 

triad  tones.  j]-,^.  rcsultant  tones  a])])earin.i4'  as  black  notes.     Xc 


Fig.    80. 


nT-^ 

•p   T'-^ 

^^    1     - 

rf-vri 

*: 

*:        1 

<^-—  i^ 

-^ — !>♦- 

* 

7  i 

s 

9 

10 

u 

12 

'^~~ — r 

a 

u. 

k=l 

(gS 


M 


Fi?.    82. 


Fig.    81. 

combination  of  the  tones  of  the 
minor  triad  \\a>  foimd  free  from 
(Hscordant  resultant  tones,  so  that 
the  three  best  ])o-^iti(.)ns  are  tlvjse 
of  l--ig.  82._ 

Tlie    major    and     minor     triads 
f(;rm  the  basis  of  our  harmonic  s_\stem.  since  tliex-  are  the  chief 
Other  chord  Hican^    of    e>tabh .-^liiui.;-    tonaht}-    and     i'urni-hini;- 

formations.  point-    of    re])ose.       I'.y    adding    other    third.-    to 

tlu'se,  t-hords  of  the  sci'Liith.  itiiilh.  dczcnt/i.  and  thirtcmth 
are  built  up,  all  oi'  ^•ar_\  in,::^'  de,^rees  of  dissonance.  Abidern 
nui-ician-  dis])]a\'  their  skill  b\-  the  continuous  u-e  of  -uch 
indeterminate  chords  to  \\ea\'e  a  web  of  lo.^icalK-dependent  l>ut 
con.-tantly-sliiftini^'  harmonies  whicli  ,-ometimes  dela\ .-  the  con- 
clusi\e  con.-onance  until  tlie  \er\-  end  oi  the  composition. 

l\evertin_^-  now  to  the  formatiijn  of  the  .-cale,  let  u.-  con- 
-idir  -ome  of  the  diftlculties  whicli  aro>e  when  the  "iu.-t" 
-cale  was  a])])lied  to  I^e\-boai"d  in>trumen!-.  i-'.\-i- 
denily,  in  order  to  modulate  from  one  -cale-ke\' 
to  another  it  -hould  lie  ])o-sible  to  reproduce 
rxactU'    in    the    <econd    kc\-   all    the    intcrx'als    of    the    first.      To 


Difficulties  in 
the  use  of  the 
"just"  scale. 


SOUND,  AND  ITS  RliLATION  TO  MUSIC.  103 

play  all  intervals  in  just  intonation  even  in  a  single  scale-key, 
ho\ve\'er.  re(|uires  two  extra  keys  in  each  octa\'e ;  for  while 
in  the  >cale  of  C,  for  instance,  the  fifths  C-G,  Ji-B,  J'-C.  and 
-i-/:  are  true.  J)  is  a  coiunia  too  sharp  for  the  true  fifth 
D-.l.  and  also  a  ])crfect  fifth  from  n  needs  an  additional  tone, 
T'i..  W  ilh  each  new  scale  there  must  he  similar  adaptations 
of  the  inter\al>,  so  that,  in  order  that  there  nia\-  he  tmre- 
stricted  modulation,  an  instrtmient  must  ha\e  at  least  seventy- 
two  ke_\  >  to  each  octa\e  I 

Accordingly,  many  attempts  were  made  to  reduce  the  num- 
Ijer  of  ke\s  1)\  slightK'  misttming  or  tcuipcriiuj  certain  tones 
and  thus  identifving  them  with  others  of  nearl\-    „    ^  . 

■^  -       bystems     ot 

the   same   ])itch.       Two   >_\stems   based   upon   this    "tempering." 
princi])le.    each -of    which    emi)lo_\s    hut    thirteen    keys    to    the 
octave.  es])eciall\-  claim  our  attention. 

In  the  first  or  nicaii-tuiic  tcinpenuiiciit,  the  upper  tones  of  all 
the  hfths  in  the  ascending  circle  ( ]^age  ^)2)  are  flatted  a 
ciuarter   of   a   comma   each,      'fhe  ptu'itv   of   the   ,. 

1  '  -  Mean-tone 

major  thirds  is  thus  ])reserved.  so  that  condititms  temperament, 
result  exactl}'  the  op])osite  of  those  in  the  scale  of  I'x'thagoras 
(page  '^2).  \vhicli  kept  the  fifths  true  while  mistuning  the 
major  thirds.  \\\  ttsing  this  s}'stem  t<jlerabl\-  i)ure  intonation 
is  possible  in  six  scale-kevs.  hut  modulation  into  the  remain- 
ing scale-ke}'s  is  impossible  since  their  major  thirds  are  hoi)e- 
lessl\-  out  of  tune.  Xex'crthele-.^  the  mean-tone  tem])erament 
had  a  wide  \'ogue.  and  was  emploxed  for  organ-  even  to  the 
middle  of  the  last  century. 

In  the  system  of  ccjual  tciiif'craiiiciit  now  in  general  use 
the  octave  is  di\'ided  into  tweh'e  stich  ])arts  that  each  bears 
the  same  ratio  to  e\'er\-  other.      In  conseciucnce,    „      , 

'  tqual 

everv    interval    i-    slightly    mi^tuned    excei^t    the    temperament. 
octa\-e.      b)Ut.  on  the  other  hand,  a  great   ad\'.'intage  is  gained 
in   the   fact   that  an   entirely    free  interchange   of   scale-ke\s   is 
made  ])ossible.  since  a  scale  of  preci<el\-  the  same  intervals  can 
be  constructed  from  each  tone  as  a  basis. 

In    I-~ig.    83    the    discord    due   t  >    tenijU'rament    is    -hown    >  ai 


104 


SOUND.  //A7)  ITS  RELATION  TO  MUSIC 


! 


1  lelmholtz"s  diagram.     The  i)Osilions  of  tones  in  just  intonation 
Comparison  are  indicated  bv  short  verticals  on  the  lower  hor- 

of    different  .  i      i-  i  -        i 

systems.  izontal    hne ;    tliose    ot    the    tones    m    mean-tone 

temperament  by  the  dotted  verticals;  and  those  of  the  tones 

in  equal  teinj>eranient  by  the  long  verticals  below. 

Although    recognizing    its   a\-ailabilil_\-    scientists    for    a    long 

time  oi)pose(l  the  general  adoption  of  e(|ual  temperament  on 

account  of  its  mathematical   inaccurac}-,   regard- 
Attitudes  .       .  .  . .  '  ,  .    ' 
toward   equal        uig  it  as  suuplv  a  make-slult  until  something  het- 

temperament.  "  '      .  .     .  \ 

tcr  could  l)e  devised.  Musicians  general]},  how- 
ever, from  r.ach  onward,  have  hailed  it  with  acclaim,  recogniz- 
ing its  enormous  jjossibilities  in  the  direction  of  added  musi- 
cal resources.  They  have  pointed  out  that  scales  are  chosen 
cssentiallv  for  .'esthetic  effect,  and  tliat  this  elTect  should  not 
be  fettered  b\-  mere  mathematical  con.siderations.  Lhi(|ues- 
tional)ly  the  o])ening  of  the  door  to  unrestricted  shifting  of 
tonality  has  been  the  cause  of  the  wonderful  ad\ance  in  musical 
ex])rcssion  during  the  ])ast  two  centuries;  and  in  \'iew  of  this 
dcvelo])ment  the  slight  (le\-iation,  scarcelv  ])erce])tible  even  to 
cxi)ert  ears,  of  the  e([ually-<em])cre(l  scale  from  the  theoretical 
tones  seems  almo>t  negligible. 

Then,  too,  the  adoption  of  a  standard   scale  for  all  musical 
use>  i.^  of  great  achantage.      It  lias  been  suggested  that  music 

in  its  purelv  vocal    forms  or  as  rendered   bv  the 

Advantages  .  ',,,,,  •        • 

of  a  uniform         stnug  f|uartet  should  be  kejjt  m   pist  intonation. 

scale.  r.  1         1  1      •  11 

out    kevljoard    instruments    are    now    so    closely 


SOUND.  AND  ITS  RELATION  TO  MUSIC  105 

connected  with  all  other  fornis  of  music  production  as  to  make 
the  adoption  of  an  altered  intonation  for  special  situations 
well-nigh  impossihle.  Orchestral  instruments  of  fixed  pitch 
are  accordingly  tuned  to  the  ecfually-tempered  scale,  to  which 
the  players  of  stringed  instruments  conform  without  difficulty. 
Indeed,  ahsolute  adherence  to  just  intonation  is  not  easy  for 
violinists,  who  so  far  violate  scientific  conclusions  as  habitually 
to  play  a  sharp  tone,  such  as  f^,  higher  in  pitch  than  its 
corresponding  flat  tone,  or  G"b.  With  singers  alone,  therefore, 
is  just  intonation  optional;  and,  owing  to  the  prevalence  of  ac- 
companied vocal  music,  it  is  doubtful  if  many  take  advantage 
of  the  privilege.  Certainly,  until  theorists  furnish  something 
palpably  better,  the  equally-tempered  scale  will  continue  to 
justify  its  name  by  pursuing  its  way  serenely  amid  the  many 
adverse  criticisms  with  which  it  has  been  assailed. 


106  SOUND,  AND  ITS  RELATION  TO  MUSIC 

SUMMARY. 

Scales  have  l^een  formed  somewhat  arbitrarily,  although  the 
characteristics  of  a  scale  are  generally  found  within  the  com- 
l)ass  of  an  octave,  and  the  intervals  of  a  whole  step,  a  perfect 
fourth  and  a  perfect  fifth  arc  frccjuentlv  recognized. 

V>\  the  word  interval  we  mean  the  ratio  Ijctween  the  vibra- 
tion numbers  of  two  tt)ncs. 

The  (Ireek  s}'stem  of  diatonic  scales  was  followed  out  in 
the  earl\  scales  of  the  Christian  Church.  'Jdiese  latter  were 
iinallv  superseded  by  our  major  and  minor  scales,  the  intervals 
of  which  were  fixed  by  theorists  in  riccordance  with  the  as- 
sumption that  consonance  is  produced  by  simple  vibration 
ratios. 

llelmhultz  was  the  first  to  ex])lain  the  reason  for  this  doc- 
trine b\-  showing  that  consonance  and  dissonance  are  dependent 
on  the  absence  or  presence  of  disagreeable  beats. 

The  major  and  minor  triads  are  the  onl\-  consonant  chords 
in  our  musical  sx'stem,  and  therefore  llie  oiilv  ones  exi)ressing 
finality.  ldie_\-  are  emplowd  in  a  \ariet\-  of  combinations,  ot 
which  but  few  are  theoreticalK'  ])erfect  in  their  consonain-e. 

"just"  intonation  is  im])racticable  for  ke}!)oard  instruments 
because  of  the  impossil)le  number  of  ke\'s  re(|uired  to  ])fe^er\e 
the  purity  of  all  intervals.  The  svstem  of  mean-tone  tem])era- 
ment  wa--  long  ])re\alent,  but  was  fmalb;  superseded  b}-  that 
of  e(|ual  tem])erament. 


KKbKkbA'Cl-:  J  J  ST. 

I/chiilioit::.  I'art?  2  and  3. 

Ziiluii.  ChapttT  10. 

luirtnu.   (  hapter  0. 

1 1  arris.  (  liapttT'^  5.  14-17. 

l!r(  ntllimisc.  ('ha]>t(.Ts  13.  15.  16. 

/'<'U\    I'ari^  _'  and  3. 

Lai'i</ii(u\  ('lia])tLr   1,   D. 

Ihinics.  Chapters   13,   14,   Appendix  2. 

Cafchpddl,  (.'hapter  7. 


SOl'ND,  AND  ITS  RELATION  TO  MUSIC  107 

Sfo)ic.  Chapter  7. 

Poyntiny  and  Thouipsoii,  Chapter  10. 

Tyndall.  ChaptiT  9. 

Blascnia.  Chapter  7. 

Taylor,  Chapters  8,  9,  10. 


CHAPTER  VIII. 

The  Ear  axd  the  \^oice. 

Two  of  the  organs  of  the  human  body  are  intimately  re- 
lated to  the  phenomena  of  sound.  The  first  of  these,  the  car. 
„  collects  the  sound-vibrations  from  the  surround- 

Human    organ 

of   sound.  jjig  atmosphere  and  transmits  them  to  our  con- 

sciousness ;  while  the  second,  the  voice,  is  by  far  the  most 
wonderful  known  instrument  for  tone  production.  Without 
the  organ  of  hearing  all  the  external  movements  which  have 
been  described  would  exist  for  us  in  vain,  and  we  should  live 
in  a  silent  world,  while  without  the  voice  the  communication 
of  thought  by  speech  and  the  outpourings  of  the  soul  in  song 
would  be  impossible. 

If  we  examine  that  marvelously  delicate  organism,  the  ear, 
we  will  discover  that  it  embraces  three  well-defined  sections, 
„,  which  mav  be  called  respectivelv  the  outer,  the 

Three  -  '-  ■  ■ 

divisions  of  middle,  and  the  inner  ear.     Of  these  the  simplest 

the    ear:     first,  ' 

the  outer  ear.  f,,  Understand  is  the  outer  ear.  This  comprises, 
first,  the  shell-shaped, 
cartilaginous  lobe 
(  Mg.  84,  L  ) .  which 
receives  the  sounds 
in  much  the  same  way 
as  does  the  bell  of  a 
trumpet.  Leading 
from  the  lol)c  inward  ^-"y^^^'^^f^: 
and    slightly    forward   ^^xT^  " 

is  the  s  o  m  e  w  hat 
crooked  tube  of  the 
auditory  ca)ial  (  I'ig.  84,  .IC).  about  IL;  inches  long,  of  which 
the  wall  is  (if  cartilage  for  nearly  half  its  length  and  of  bone 
the  re>t  of  the  way.  A  number  of  fmc  hairs  and  the  car- 
wax  secreted  b\-  glands  within  protect  this  from  the  intrusion 


84.     Transverse  section  of  the  car. 


SOLWD,  ,L\'D  ITS  RliLAl'lOS  TO  MUSIC 


109 


of  external  objects.  At  the  end  of  the  canal,  stretched  slant- 
wise and  ctu'ving  inward,  is  the  thin,  elastic  membrane  known 
as  the  drumskiii  {V\\^.  84 /J  ) .  which,  like  the  dia[)hragm  of  the 
telei)hone  and  phonograph,  is  cjuick  to  respond  to  every  kind 
of  sotind-wave  which  impinges  upon  it. 

ISehind  this  membrane  is  the  middle  ear  or  drum  cavity, 
hollowed  otit  in  the  thick  bony  part  of  the  sktdl.  On  the 
side    of    this   cavitv   opposite    the    drumskin    are   „,         .,,, 

■'  1  i  The     middle 

two  >o-callcd  zcindu-K's,  each  of  which  is  covered  ^^''• 
also  by  a  membrane.  The  lower  of  these,  the  round  zcindozv 
(Fig.  84  R)  is  abotit  the  size  of  a  pin's  head,  while  the 
upjjer  or  oral  z^'iiido:^'  (.I'ig.  84  O)  is  somewhat  larger.  In 
the  lower  wall  of  the  cavitv  is  an  opening  from  which  the 
Eustachian  tube  (Fig.  84  ILT),  ly^  inches  in  length,  leads  to 
the  back  of  the  throat.  Whenever  we  swallow,  this  tube  is 
opened,  so  that  the  drum  cavity  is  kept  in  totich  with  the 
external  air,  and  thus  relieved  from  undue  pressure.  We 
can  appreciate  the  need  of  this  outlet  when  we  experience  the 
sensation  of  deafness  and  roaring  in  the  ear  which  results 
from  the  clogging  of  the  tube  that  sometimes  occurs  in  the 
progress  of  a  "cold  in  the  head." 

Three  peculiarly-shaped  bones  called  the  auditory  ossicles 
(Fig.  84  .10),  which  have  been  named  from  their  fancied 
resemblance   to    familiar   objects,    form    a   chain    ^, 

■'  The    auditory 

of  connection  between  the  drumskin  and  the  ossicles, 
oval  window.  These  are 
shown  more  specifically  in 
Fig.  85.  The  lower  part  of 
the  hammer  is  attached  di- 
rectly to  the  drumskin,  pull- 
ing it  slightlv  inward,  while 
the  upper  part  articulates  with 
the  anvil.  This  bone  in  turn 
is  attached  on  its  lower  side  to 
the    apex    of    the    stirrup,    of  ^'S-  ^^• 

which  the  base  is  fastened  to  the  membrane  of  the  oval  win- 


llammer 


no  SOUXD,  AXD  ITS  RELATIOX  TO  MUSIC 

(l(i\v.  All  these  bones  together  form  a  kind  of  lever  which  re- 
])ro(luces  ever}-  motion  of  the  drtimskin  in  the  membrane  of 
the  o\al  window,  with  this  diti'erence.  however,  that  in  trans- 
mission the  \ibrations  are  diminished  in  magnitude  but  in- 
creased in  force.  As  the  membrane  of  tlie  o\al  window  is 
but  -j^-  to  TT^ij  the  size  of  the  drumskin,  this  lessening  of 
magnitude  bccome>  necessar_\-,  while  the  greater  force  is  re- 
ciuircd  to  o\-ercome  the  added  density  of  the  medium  on  the 
other  side  of  the  o\"al  window,  to  which  the  \'ibrations  must 
next  extend.  W'e  >hould  also  mention  two  important  muscles 
Contained  in  the  drum  cavitx ,  which  have  the  ])ower  (.)f  tight- 
ening the  memljranes  respecti\elv  of  the  drumskin  and  of  the 
o\al  window. 

It   i.--   the   inner  ear,   how  e\-er,   which   contains   the  most   im- 
portant and  complicated  -ection  of  the  hearing  apparattt>  ;  in- 
deed,  if  all   the  mechanism   of   the  external   and 

General     form  •in  i      •  •     i 

of  the  inner         uuddle  ear  Were  destro\ed,  it  nnght  \  et   he  po>- 

ear. 

>ible  tor  a  ]ierson  to  hear,  in  part  at  least,  bv 
holding  between  the  teeth  >ome  such  (kwice  as  that  mentioned 
on  page  i).  which  transmits  the  souikI  throttgh  the  bones  of  the 
head.  The  inner  ear  occujtie^  a  complex  l)on_\-  ca\'it\-  which 
is  >o  winding  in  its  cour-e  that  it  i-  called  the  labyrinth. 
Within  the  otuer  or  boiix  labyrinth  there  is  a  meml)ranou- 
.■>ack  called  the  nimil'vauous  labyrinth,  which  follows  a])])roxi- 
matel\-  the  ctnwes  i)f  the  bon\-  lal)_\Timli  and  is  onl\-  connected 
■  'A'ith  the  latter  where  the  ner\  e  tibre-^  ])a>s  between  them. 
Tb.e-e  fibres  ramif\-  over  the  stu"face  <>i  the  membranous 
labxriiith,  and  are  excited  l)\'  minute  liair>  which  ])roject  from 
the  delicate  inner  lining  I'f  the  nieiiibrane,  and  which  are 
t!uni-el\'es  set  in  motion  by  ctiiliths.  or  niiiitite  .^r)lid  jjarticles 
like  grains  of  sand.  'rbe.-~e  particle--  are  lloating  in  a  waterv 
tlttid  called  the  rinlclyjiif'h.  which  tills  the  membraiiotis  lab\'- 
rinth,  and  the  latter  is  nearl\-  surrotmded  liy  a  similar  tiuid 
called  the  pcrilynij^Ji. 

Thi-^   perihni]ih    is   in   direct   contact   with   the  o\'al    window 
of  the  middle  ear  in  the  7'estibulc  (  b^iir.  '^A  Tl  which  form-  th* 


SOUND,  JX!)  ITS  h'l:L.ITIOX  TO  MCSIC 


111 


entrance  to  the  inner  ear  and  also  the  centre  of 

I)  1    •  1  111  1      '^^^    vestibule 

Its  structitre.      hranclimg-  ui)\var(l  and  backward    and  semi-cir- 

1  Ml  11  11      1  •        cular     canals. 

trcjin  the  vestibule  are  tlie  three  so-called  soiii- 
cii'ciilar  canals    (  I'iy.  84  SX'),  which   have   live  openings  into 
it.     These  canals  are  beliexed  to  be  the   seat  of  the  sense  of 
e(|uilibriuni,   and   are  therefore   not  intimateU-  concerned   with 
our  discussion  of  the  sense  of  hearing. 

It  is  in  the  cochlea  (  I"ig.  (S4  C  ),  situated  forward  and  down- 
ward from  the  x'estibule,  that  sound-percepti(jn  i>  esi)eciall\- 
located.       This     cochlea     ( meaning     ■'slieU"  )     i>    .^^^  ■  ■  r 

•~  Divisions    01 

named  from  its  resemblance  t(^  a  .^naiI-shell.  It  ^^"^  cochlea. 
consists  in  a  tube  which  winds  two  and  one-half  time>  around 
a  central  bonv  axis  and  terminates  in  a  closed  tip.  A  bom' 
partition  called  the  lamina  spiralis  projects  into  the  ttibe  for 
about  two-thirds  of  its  diameter,  the  other  third  being  spanne<l 
by  a  meml)rane  called  tlie  basilar  iitcjiibraiic.  This  partition 
end-  just  Ijcfore  the  ti])  of  the  tube  is  reached,  so  that  the  tube 
i-  dixided  through  nearlv  its  entire  length  into  two  chambers. 

the  scala  rest  ibid  i 
and  the  seala  tym- 
pani.  that  are  fdled 
with  the  periKniph 
and  that  commu- 
nicate at  the  tip  of 
the  tube.  One  of 
these  c  h  a  m  b  e  r  s 
o])en<  into  the  ves- 
tibule while  the 
other  is  directl\ 
connected  with  the 
membranes  of  the 
round  wind(jw. 
T  h  e  latter  thu- 
serves  as  a  kinrl  of 
builer  for  the  \'i- 
brations  which.  Ix-- 


Fig.    86.    Trail. --versu  section  of  the  whorl  of  the  Cochlea. 


^chlearis    Mf^r' :' 


112  SOL'XD,  AXD  ITS  RELATIOX  TO  MUSIC 

ginning  at  the  vestibule,  travel  up  one  of  the  chambers  and 
down  the  other,  and  which  would  otherwise  be  deadened  bv  the 
lack  of  a  yielding  surface  from  which  to  reljound.  A  small 
canal  containing  end(jlymph  is  formed  bv  the  incmbranc  of 
Rciss)icr,  which  extends  from  the  lamina  spiralis  to  the  otiter 
wall  of  the  tube.  The  positions  of  all  these  parts  can  be  bet- 
ter understood  l)y  reference  to  Fig.  86,  which  shows  a  trans- 
verse section  of  the  cochlean  tube. 

In  the  region  of  the  basilar  membrane  a  \-er}-  complex  struc- 
ture is  found.     The  outer  portion  of  this  membrane  is  com- 
])osed  of  at  least  3000  radial  fibres  imljedded  side 
the  basilar  bv  sidc  and  growmg  longer  trom  the  entrance  of 

membrane.  '  .  . 

the  tube  to  its  tip,  so  that  at  the  latter  end  they 
are  ten  times  as  long  as  at  the  former.  It  is  thought  that 
these  fibres  are  tuned  to  the  various  degrees  of  sound-waves, 
so  that  these  waves  sweeping  over  them  set  into  sympathetic 
vibrations  the  fibres  which  agree  whh  the  waves  in  pitch,  and 
which  then  vibrate  with  an  inten>ity  proportionate  to  that  of 
the  exciting  force.  \\"hile  thus  pitch  and  i)itc)!sify  are  deter- 
mined, (jualitx  results  from  the  combination  of  the  diverse 
sound-components. 

Intermediary  agents  between  these  fibres  and  the  auditory 
nerve  which  enters  at  A',  b'ig.  84.  and  which  winds  it^  way 
„,  thr(.)Ugh  the  laminar  sHralis,  are  the   ori/ans  of 

The   organs  ^  '  ^/  .' 

°^   ^°''*'-  Corfi.    two   ranks   of    fibres   at    the   base   of    the 

basilar  membrane,  N/hich  lean  over  against  one  another  like 
the  rafters  of  the  peaked-roof  of  a  house.  Xerve  cells  sur- 
round these  fibres  both  on  the  exterior  side  and  in  the  canal 
between. 

The  exceeding  delicac\-  of  the  strticture  of  the  cochlea  can 
be  estimated  when  we  reflect  that  its  entire  coil  has  a  diameter 
^.        .  of  but  one-ciuarter  <if  an   inch,   and   that   if  un- 

Dimensions  ^ 

of  the  cochlea,  y, ,\]^,\  j^^  length  would  be  about  1  '  ^  inches.  Fig. 
f^~  gives  an  enlarged  sectional  \iew  of  the  inside  oi  the  ear, 
showing  the  proportions  of  the  ])arts.     As  in  Fig.  84..  iC   is  the 


SOUND,  AND  ITS  RELATION  TO  MUSIC 


113 


ET 


auditory  canal,  D 
the  drumskin,  .10 
the  auditory  os- 
sicles. ET  the  Eu- 
stachian tube,  O 
the  oval  window, 
R  the  round  win- 
dow, SC  the  semi- 
circular canals,  and 
C   the   cochlea. 

A     sound  -  wave 
striking    the    outer 
ear  thus  makes  its 
way     throut,di     the 
auditorv  canal  and  sets  into  vibration  the  drumskin,  wdience 
it   is    carried    bv    the    auditory    ossicles    to    the    oval    window. 
The  increased  force  which  it  i^^ains  in  this  trans-    bourse  of  a 
mission  suffices  to  set  into  motion  the  perilymph    ^^rough^he 
in  the  vestibule  of  the  inner  ear.  which  in  turn    ^*'■• 
conveys  it  around  the  curves  of  the  cochlea  until  it  discovers 
and  sets  into  A'ibration  the  proper  membranous  fibre.    Through 
the  organ  of  Corti  the  impulse  strikes  the  auditory  nerve  which 
carries  it  to  the  brain,  whence,  in  some  inexplicable  manner, 
it   passes   into  our  consciousness. 


Fig.    87.   Section  of  the  middle  and  inner  ear. 


Four  factors  are  involved  in  voice-production,  namely,  the 
lungs,  which  act  as  the  motor,  the  vocal  cords  or  vibrator,  a 
number  of  cavities   which   constitute  the   rcson- 

1  1  •  r  1-r     ■  11         Factors    in 

ator.  and  a  mechanism  tor  modiivmg  or  check-    voice-pro- 

1  11      1      1  •       I  '  duction. 

ing  the  tone  called  the  articulator. 

Xearly  the  whole  of  the  chest  cavity  is  occupied  by  the  two 
lungs.  \\'hen  these  are  expanded  the  outer  air  is  drawn  into 
them    in    inspiration,    and    when    thev    are    con-    „,     , 

'  •  The    lungs 

tracted  the  air  is   forced  out  in   expiration.      Tn    and  wind-pipes, 
the  latter  process  the  air  passes   from  the  lungs  through  the 


114 


SO[\\D.  .IXD  ITS  KELATIOX   TO  Ml'SIC 


The    larynx. 


zci)i(if'i/'c.   a  crirtila,c,nnous  lube    four  or   five  inches  long,  into 
tlie  larynx,  there  coming  into  contact  with  the  vocal  cords. 

I'he  laryn.r  nr  :'(:icc-ho.v  is  a  triangular  tube  composed  of 
several  ])ieces  of  cartilage,  the  front  edge  ap])earing  in  the 
ihrcjat  as  the  familiar  "Adam's  Ai)])le."  Within 
thi>  tube,  ■-tretching  from  front  lo  back,  are  the 
two  folds  of  meml)rane  known  as  the  z'ocal  cords.  These 
are  attached  to  tlie  outer  wall^,  and  are  free  <m\y  on  their 
inner  sides,  where  there  i-  conseriucntK-  an  ()])enmg,  called 
the  f/loffis.  \'<y  means  of  a  iuini.l)er  oi  mu<cle>  which  act  au- 
tomaticallx'.  the  xocal  cords  n.dv  be  expanded  or  contracted  iu 

Frontal  sinus 


Vocal  cords 


Fig.  88.  Section  of  the  head  and  Uiroat  locating'  tlie  organs  of  speech  and  sonjf, 
in  iudinu  the  upper  resonators.  Tlie  important  ma.xillary  sinus  cannot  well  he  shown. 
It  i-.  found  within  the  nia.xillar.v  hone  (clicek  bone),  'riic  inner  end  of  the  line  marked 
,\'i;  ,:  ■  -  a:  // r  locates  it. 


SOUMD.  .I\n  ITS  RliLATION  TO  MUSIC  115 

a   variety   of    ways,   and    the   "diink    of    the   glottis"   may   be 
widened,  shortened,  or  narrowed  until  it  is  entirely  elosed. 

In  ordinary  l)reathing"  the  vocal  cords  remain  wide  apart, 
so  that  the  air  passes  between  them  freely.  When,  however, 
t(Mie   is   desired,   the   cords   are   brought   together 

1  •       •  11      1    •  1-1  r    1-      1         Action    of 

SO  that  the  an"  is  expelled  ni  a  multitude  oi  little    the  vocal 

,,,,  -  cords. 

pults,  as  With  a  reed.  1  hese  putis  generate  a 
tone  which,  though  feeble,  is  yet  sufficient  to  set  the  resona- 
ting cavities  into  sympathetic  vibration.  The  loudness  of  the 
tone  is  atiected  by  the  amount  of  l)reath  ])ressure  on  the  \ocal 
cords,  and  the  pitch  is  determined  bv  their  tension  and  ])osi- 
tion  relative  to  each  other. 

We  have  now  to  consider  the  rrsoiiafijuj  canities,  the  sha])e 
and  adjustment  of  which  have  so  important  an  eti'cct  on  the 
(|U<'i!it\'  and  ouantit\-  of  tone.     Reference  to   b^ig. 

oo  Mi  ,  ,  ■         •    •  -       1  1  .The  epiglottis 

(SN   Will   make   the   ])osilions  ot   these   clear.      At    and  the 

.,.,.,       pharynx. 

the  t(^])  of  the  lar_\-nx  is  a  lid  or  cf'ujlottis.  which 
closes  it  in  the  act  of  swallowing  and  also  aids  in  deyeloi)ing 
tlie  generated  tone.  Xext  ccnnes  the  cavity  at  the  l)ack  of 
the  mouth  called  the  pharxii.v.  which  nia\-  be  changed  materially 
in  sha])C  b}-  muscular  action,  and  the  walls  of  which  come 
together  when  swallowing  takes  place.  If  the  phar\"nx  is  kept 
as  far  t)\)(.'u  as  i)ossible  its  "esonance  greath'  enriches  the  v(x~al 
tone.  Into  it  o])en  the  two  luistachian  tubes  connecting  with 
the   ears    (])age    10<)). 

Two  ])assages  from  the  ])harynx  lead  the  one  into  the  iiioiitit 
rarity  and  the  other  into  the  tiasa!  canities.  The  soft  palofc 
terminating  in  a  pendulous  tip  called  the  iiziila.    „,        ,, 

>^  1  1  Tile    soft 

which  can  readily  be  seen  hanging  down  in  the  pa'^te. 
back  of  the  mouth,  regulates  the  size  of  these  openings.  If 
the  soft  palate  be  forced  backward  until  the  ])assage  to  the 
nasal  cavities  is  closed,  vibrations  arc  ccmimunicated  to  the 
latter  onK-  through  the  i)alate,  so  that  a  muffled  "nasal  twang" 
results.  When,  however,  the  palate  is  allowed  to  hang  frceh'. 
with  only  such  changes  in  ])osition  as  are  necessar\-  to  keep 
the  cavities  in  tune  with  the  generated  tone,  resonance  i<  un- 


116  SOUXD.  AXD  ITS  RRLATIOX  TO  MUSIC 

restricted  and  the  tone  vibrates  through  the  cavities  of  the 
nose  and  head. 

The  roof  of  the  mouth,  or  hard  palate,  with  the  soft  palate 
behind  it  form  the  floor  of  the  two  nasal  cavities.  These  are 
„,  ,  separated  bv  the  bonv  i)artition  v.'hich  forms  the 

The    nasal  '  -  -     i 

'^^^'*'^^-  bridge   of   the   nose,   and   into   each   one   project 

three  spongy  bones  which  serve  to  increase  the  surface  area. 
This  surface  is  lined  throughout  with  mucotis  membrane  cov- 
ered with  continually  moving  hairs  or  cilia,  hv  means  of 
which  the  air  entering  the  nostrils  is  ])uritied,  tempered  and 
moistened  before  proceeding  to  the  lungs. 

A  number  of  air-chambers  or  sinuses  are  hollowed  out  in  the 
bones  beside,  above  and  behind  the  nasal  cavities.  As  these 
„,      .  possess    passages    of    communication    with    each 

The   sinuses  '  i  & 

of  the  head.  other    and    with    the    nasal    cavities,    thev    form 

valuable  adjuncts  to  tlie  resonating  resources.  Since  the  nasal 
and  head  cavities  cannot  be  changed  in  form,  their  resonating 
powers  will  be  determined  by  their  natural  size  and  shape  and 
their  freedom  from  obstructions. 

While  the  nasal  and  head  cavities  are  the  chief  factors  in 

producing  strength  and  purity  of  tone,  the  mouth  cavity  and  its 

adjacent  parts  have  as  their  distinct  function  the 

The   mouth.  , .  ,  .  .     , 

modifications  ot  the  tone  m  articulation.  A  dome- 
shaped  roof  consisting  of  the  hard  palate  surmounts  the 
mouth,  bounded  in  front  and  on  either  side  bv  a  row  of  teeth 
which  furnish  resistance  to  the  tongue  and  lips  in  forming 
consonants.  The  free  lower  jaw,  furnished  wdth  a  correlative 
row  of  teeth,  renders  mobile  the  tongue,  which  is  attached  to 
it  directly  by  muscles  and  indirectly  by  the  Iiyoid  or  tongue 
hone.  Evidently  a  relaxed  lower  jaw  and  flat  tongue  favor 
resonance  by  enlarging  the  mouth  cavity. 

During  articulation  there  is  a  constant  muscular   interi)lav 
between  the  tongue  and  the  teeth,  which  by  their  varied  posi- 
tions  modifv   or   interrupt   the   tone   to   produce 

Articulation.  .     .        '   ^.  i    •    i 

most  of  the  ettects  which  we  translate  into  words. 
Changes  in  the  shape  of  the  mouth  cavity  as  a  whole  are 


SOUND,  AND  ITS  RELATION  TO  MUSIC  117 

responsible  for  the  tone-cjualities  known  as  vozvcl  sounds. 
Experiments  have  proved  that  each  vowel  has  a  jj^^yre  of 
normal  pitch  Avhicli  is.  moreover,  the  same  for  ^^^  vowels, 
all  voices.  That  of  oo  is  the  lowest  and  that  of  ee  the  highest, 
the  others  ranging  between  these  limits,  with  ah  occupying 
a  middle  position.  I'^ach  vowel-characteristic  may.  however, 
be  extended  u])  and  down  from  its  normal  pitch,  although  cer- 
tain ])itches  are  more  favorable  than  others.  Oo  and  oh,  for 
instance,  are  more  easily  sung  at  a  low  pitch  and  ai  and  ee  at  a 
high  one,  while  ah  lends  itself  readily  to  the  entire  compass. 

A'owel-qualit\-  is  modified  in  a  variety  of  ways  by  conso- 
)iaiits,  which  are  reallv  forms  of  obstruction  to  the  simple 
\()wel  sounds.      IJesides  the  tongue  and  lips,  the    ..  ,         , 

•^  i     '  Nature    of 

organs  of   articulation,  by  which  these  oljstruc-    consonants, 
tions   are   effected,   include   the   teeth   and   the   hard   and   soft 
palates,  while  the  facial  muscles  may  also  be  called  into  play 
as  an  aid  in  the  process.     .According  to  a  classification  that  is 
useful  for  singers  the  consonants  may  be  grouped  as  follows: 

1.  the  explosives,  such  as  p,  t,  f,  %',  in  which  the  obstruction 
is  complete; 

2.  the  semi-explosives,  such  as  b,  d,  and  hard  and  soft  g,  in 
which  the  obstruction  is  only  partial; 

3.  the  pennanents,  like  /.  ;;f.  and  n,  of  which  the  sound  can 
be  prolonged  indefinitely. 

The  aspirate  sotmd  of  h  is  formed  bv  allowing  the  breath 
to  flow  through  the  glottis  before  the  tone  is  ])roduced. 

Another  classification  grotips  the  consonants  according  to 
the  place  in  which  thev  are  i)roduced  :  for  instance,  m,  h,  p, 
made  with  the  lips,  are  termed  labials;  f,  d.  and 

r  1     1  -1  -1         Labials, 

11,    lormed    b\'   pressing   the    tongue   against   the   dentals  and 

1  7  7  1-1         I  11  gutterals. 

teeth  are  dentals:  and  those  like  k  and  hard  g. 
made  in  the  back  of  the  mouth,  are  gutterals.     These  conso- 
nant sounds  are  also  used  in  a  number  of  combinations. 

There  is  no  considerable  difference  in  the  formation  of  tone 
for    the    si)eaking    and    singing    voice.      In    the    o       u      j 

'  <^  .~>      <->  Speech    and 

former,    since    distinctness    of    utterance    is    the    ®°"^- 


118 


SOUND,  AND  ITS  RELATION  TO  MUSIC 


]jrime  requisite,  the  tone-compass  is  narrow  and  the  tone  un- 
steady, wliile  in  the  hitter  definite  pitches  are  assumed  through- 
out the  natural  voice  compass.  ■■S])eecli  may  he  called  the 
prose,  and  song  the  poetry  of  vocalization."'*  Singers  often 
make  the  mistake  of  unduly  modifying  vowels  and  clipping 
consonants  in  order  to  produce  puritv  of  tone,  thus  defeating 
the  primarv  ohjcct  of  song,  which  is  to  give  a  fuller  expression 
to  the  meaning  of  the  text. 

ISesides  the  sounds  of  vowels  and  consonants,  all  kinds  of 
tone-cjualities,  hoth  good   and  had,   are  possihle  to  the   \oice. 

^     , .  ,       Trcjfessional   imitators,  indeed,  are  ahle  to  pro- 

Graphic  vocal  '  i 

'^°"^^-  duce  a  recognizable  vocal   suggestion  of  almost 

any  sound  whatever.  Some  attempts  have  been  made  to  se- 
cure gra])hic  representations  of  vocal  tones,  so  that  practical 
means  iiKn-  Ije  ])rovided  for  measuring  their  degree  of  con- 
formity to  a  given  standard.  Mrs.  Watts  Hughes,  of  T.ond(jn, 
published  a  pam])hlet  in  1891  recording  various  ex])erinients 
with  an  instrument  which  she  calls  the  Hid',l-<lioiu\  This  con- 
sists of  a  long  tul)e  having  the  large  end  bent  upward.  (  )\cr 
this  end  a  memljranc  is  stretched  on  wliich  is  stre\\'n  light, 
])asty  materials  which,  when  tones  are  sung  into  the  other  end. 
range  thcmseK-es  into  consiantl\-var\-inu  -lia])es.  whose  com- 
])lexity  is  de])cndent  on  that  of 
the  tones  to  which  the}'  re- 
s])ond.  liesides  geometric 
hgures,  delicate  flower,  tree 
and  shell  design>  are  formed, 
such  as  those  shown  in  b'ig-. 
S9.  90  and  91.  Recently,  also. 
by  a  similar  device  in  whicli 
ihe  vil)rations  of  a  rubber  dislx 
are  reflected  by  an  attached 
mirror  upon  a  rai)idl\"-mo\-inL.' 
sensiti\'e  i)late.  Dr.  AFirage.  o,f 
T^iris,  claims  to  have  secured  Fig.  89.   Dai.sy  fonn 


99V/.-/. 


-'■Rosonanre    in    Siii.uiiiL;    and    Spcakins. 


SOL'XD,  .1X1)  ITS  RliL.lTIOX  TO  MUSIC 


119 


photographs  of  the  \oicc  wliich 
show  marked  distinction-  he- 
twecn  true  and  fal>e  intonation. 
All  the  tones  ])rodttcc(l  b}'  the 
human  voice  cover  nearl\-  four 
octaves,      although    ^  , 

'  ^         Range   of 

these  limits  have  ''°'"^- 
been  considerably  extended  bv 
exceptional  singers.  Average 
voices  have  a  range  of  somewhat 
less  than  an  octave  and  a  half, 
c-      nn    ^-      *•  ;in(l     in     men     this     compas-     i- 

h  in.    90.     i-ctn  toriii  I 

about  an  octave  below  that  in 
women.  The  latter  fact  is  dtie  partly  to  the  difference  in  the 
f(M-mation    of   the    resonance   chamber^    and   ])artl\'   to   tin    di- 


Fi£ 


91.     Shell  form. 


\-crsit}-  in  the  thickness  and  extent  of  the  vocal  cord.-,  ih'  -e 
<  if  men  a\'eraging  three-quarters  of  an  inch  and  those  of  \v>  nncn 


120 


SOiWD,  AXD  ITS  RELATIOX  TO  MUSIC 


a  half  inch  in  length.  \'oices  are  classified  chietlv  according 
to  their  quality,  so  that  singers  whose  hest  tt)nes  are  high  in 
pitch  rank  as  sopranos  or  tenors,  those  who  excel  in  the  mid- 
dle tones  are  called  mezzo-sopranos  or  haritones.  while  the  low 
voices  are  classed  as  altos  or  hasses.  \'oices  of  extreme  range 
are  rare,  for  the  average  human  voice  is  of  middle  range. 
Fig.  92  shows  the  normal  limits  of  the  various  kinds  of  voices. 

COMPASS  OF  THE  SIXGLNG  VOICE 


Tenore 

•■      Tenore 

Barit 

->ne 

Bas^o 

'  "  Ba 

s^(> 

Primo 

Secondd 

Cantanle 

I'rot 

und 

Fig.    92.    Compass  of  the  singintr  voice. 


SOUND.  AND  ITS  RELATION  TO  MUSIC  121 

SUMMARY. 

The  ear  has  three  sections,  of  which  the  outer  comprises  the 
lobe  and  the  auditory  ca)ial,  lea(hng  to  the  drumskin.  Sounds 
are  transferred  from  the  drumskin  in  die  middle  ear  by 
means  of  the  three  auditory  ossicles  to  the  oval  windoz<.'. 
which  cl()>es  the  entrance  to  the  inner  ear.  In  the  latter  the 
hon\  labyrinth  is  hlled  with  a  watery  fluid  containing  the  incDi- 
bra)ious  labyrintli,  and  by  a  complicated  arrangement  in  the 
cochlea,  sound  is  communicated  to  the  auditory  nerve,  which 
conveys  it  to  the  brain. 

There  are  four  factors  in  the  voice.  The  first  of  these  is  the 
lungs,  which  as  motor  furnish  the  breath  supply  that  sets 
into  motion  the  second  factor  or  vibrator,  consisting  of  the 
vocal  cords.  The  tone  which  they  produce  is  greatly  magnified 
and  altered  in  quality  by  a  number  of  resonance  chambers, 
which  form  the  third  factor.  Tone  emerges  from  these  as 
vowel  sound,  which  mav  be  more  or  less  obstructed  by  the 
consonant  sounds  originated  by  the  fourth  factor,  namely,  the 
organs  of  articulation.  Individual  voices  differ  markedly  in 
quality  and  compass. 

REFERENCE  LIST. 

The  Ear. 
Helmholtc.  Chapter  4. 
Tyndall.  Chapter  9. 
Barton.  Chapter  6. 
CatcJipool.  Chapter  7. 
Harris.  Chapter  3. 
LaTignac.  Chapter  1,  C. 

The  Voice. 

Hehnliolic.  Chapter  5. 
Broadhousc.  Chapter  10. 
Barton.  Chapter  8. 
Laz'igiiac,  Chapter  2,  A. 

The  following  books  on  singing  have  valuable  data  concerning 
acoustics : 


12Z  SOUND,  AND  ITS  RELATION  TO  MUSIC 

Fillebrown,  "Resonance   in   Singing  and   Speaking."    (Oliver   Ditson 

Company,   1911.) 
Curtis.    "Voice    P)uilding    and    Tone    Placing."      (D.    Appleton    and 

Company,  1909. ) 
Brox^'uc  and  Belntkc.  "Voice,  Song  and  Speech."  ( G.  Putnam's  Sons, 

1883.) 
Standard  medical  works,  like  Gray's  Anatomy  and  Waller's   Physi- 
ology may  be  consulted  for  more  minute  details  concerning  both  organs. 


CHAPTER  IX. 

AlUSKAl.    I  NSIRL'MKNTS. 

While  the  voice,  most  marvelous  of  all  instruments,  has 
been  the  common  property  of  ail  men  in  all  ages  and  climes, 
artiticial  instruments  have  taken  on  so  endless  a 

r     r  1  I  r      1  Variety    in 

vanetv  oi  lorms  that  a  mere  catalogue  or  them   the  construction 

1  i'    -11         1  AT-        1      11  °^   instruments. 

would  lill  a  large  vokmie.  W  e  shall  content  ottr- 
selves,  therefore,  with  examining  the  most  important  of  those 
of  the  present  day,  and  with  studying  simply  the  acoustic 
peculiarities  of  these,  leaving  to  specialized  works  the  treat- 
ment of  mintite  details  of  their  construction  and  technic.  i'^or 
the  most  part,  instriuncnts  lune  asstmied  their  hnal  sha])es  as 
the  restilt  of  many  experiments,  in  which  scientific  theories 
have  played  but  a  small  part.  When  viewed  in  the  light  of 
acoustic  laws,  however,  thev  have  almost  always  been  fotmd 
to  conform  to  these  laws  and  to  furnish  interesting  examples 
of  their  practical  a[)plication. 

One  kind  of  instrtmient  is  distingtiished  from  another  by 
the  Diatcrials  of  which  it  is  made,  its  form,  compass,  sustaining 
power,  decjrccs  of  possible  iiitensitw  and  csijcci-   „,       ,    .   . 

'  ./  .'     i  .  1  Lnaractenstics 

ally  its  quality.  Again,  some  instruments  are  °^  instruments, 
restricted  to  the  production  of  one  tone  at  a  time,  while  on 
others,  like  tlie  violin  antl  'piano,  tonal  combinations  are  pos- 
sible. As  with  the  x'oice,  each  instrument  must  have  a  motor 
for  exciting  it  into  action,  a  ribrator  generall\-  accom})anied 
by  a  resonator,  and  a  meclianism  for  re(/ulatin</  the  pitch  and 
other  characteristics  of  the  tone. 

\\  ith  all  their  diver>ity,  instruments  are  readilv  divisible 
into  a  few  well-defmed  ty])es.  Foremost  among  these,  on  ac- 
count   of    their    wide    range,    facile    manii)ulation    „ 

•^  i  Types   of 

and    general    availabilitv,    stand    the    instruments   instruments: 

"  -  those  with 

icith  stretched  strings.     Let  us  first  discuss  those   strings. 

123 


124  SOUND,  AND  ITS  RELATION  TO  MUSIC 

of  this  class  in  which  the  strings  are  plucked,  either  by  the 
fingers  or  by  a  device  called  a  picctrnm. 

A  weak-toned  instrument  chielly  used  for  accompaniments 
is  the  (jiiitar.  This  has  six 'strings,  the  three  upper  of  catgut 
The  guitar.  and  the  others  of   silk  wound  with  silver  wire. 

■♦*- 
tuned  thus:     .V"'    *>  ^    Its  notes  are  always  written  an  octave 

higher  than  played.  The  strings  are  plucked  by  fingers  of  the 
right  hand  while  those  of  the  left  varv  the  scale-notes  by  press- 
ing the  strings  against  metal  bars  or  frets  which  cross  the 
neck  at  the  proper  intervals.  Upper  partials  or  '"harmonics" 
can  be  played  bv  touching  the  strings  lightly,  instead  of  press- 
ing them  upon  the  frets,  at  one  of  their  nodal  points. 

The  guitar  often  accompanies  the  maiidolin.  a  pear-^haped 
instrument  also  fretted  and  having  eight  strings  tuned  in 
The  mandolin.       uuison  pairs  to  the  same  tones  as   those  of  the 


violin,   thus:    ^^^S^     A   ])lcctruin  of   horn   or   tortoise-shell 


rsrr 


held  in  the  right  hand  excites  the  strings.  While,  as  with  all 
stringed  instruments,  the  inferior  limit  of  the  c<jmpass  is  the 
tone  of  its  lowest  string,  the  ui)i)er  limit  for  the  mandolin  is 
about  c'" ,  an  octave  above  the  tone  of  its  highest  open  string. 
Bright  upper  partials  give  a  nasal  quality  to  the  tone,  which 
is,  however,  light  and  delicate  in  character. 

r.y  far  the  most  im])ortant  instrument  of  this  group  is  the 

Jiarp.  which  has  a  large  range  and  an  ethereal  tone  that  is  fre- 

C|uentl\-  cm])l(ne(l  with  much  charm  in  (irchestral 

The  harp.  ,   •'        •  '  ,,  -  ,  1  t  i. 

combinations  as  well  as  tor  soio  work.  Its  4o 
strings  are  tuned  diatc^nicall}-  in  the  scale  of  C'^  through  a  com- 
pass of  6' J  octaves,  which  extends  from  ( ''''  to  f"^^'.  \W  means 
of  sc\-en  pedals,  each  of  whicli  niav  raise  a  gi\en  tone  a  half 
or  whole  >tep  throughout  the  comitas-.  the  tuning  may  be 
"set"'  for  an\-  major  or  miuiu-  scale  other  than  the  origin.al 
one.      Running   [passages    in    broken    chords,    called    arpcijgins 


SOUND,  AND  ITS  RELATION  TO  MUSIC  125 

from  the  instrument  itself,  are  characteristic  of  the  harp.  By 
touching  a  string  lightly  in  the  middle  with  the  palm  of  the 
hand  and  pktcking  it  with  the  hrst  two  fingers  of  the  same 
hand,  clear  and  beautiful  harmonics  are  evoked. 

In  the  case  of  the  guitar  and  mandolin  the  natural  tone  of 
the  strings  is  strengthened  by  sympathetic  vibration  of  the 
bodv   of    the   instrument   and   the   air   within   it,   ~,   . 

'    Their 

while    with   the  harp   a   similar   effect   is   gained   resonators. 

by   the   sound-box   on   which   it   stands,   and   which   acts  as   a 

resonator. 

Instruments  with  struck  strings  have  as  their  chief  repre- 
sentative the  hard-worked  pianoforte.  Eighty-eight  strings  of 
different  pitches,  of  which  all  but  the  verv  lowest 

1111  1  111  '  1  '^^^  pianoforte. 

are  doubled  and  many  are  trebled,  extend  at 
semitone  distances  over  a  compass  of  7ji  octaves,  from  .-in 
to  c^'.  Their  t(jnes  are  reinforced  bv  a  thin,  flat  sounding-board. 
]"\dt-covered  hammers  are  driven  against  the  strings  by  a  key 
mechanism,  to  induce  vibration,  and  by  the  clastic  covering 
and  rounded  ends  of  these  hammers  the  metallic  overtones  are 
suppressed  which  are  produced  when  a  hard  object  strikes  a 
string  at  a  single  point.  By  making  each  hammer  attack  its 
string  at  ^/7  or  V^^  '■'^  its  length  from  the  end,  other  disagree- 
able upper  partials  are  avoided    (page  58). 

The  soft  pedal,  bv  moving  the  action  along  in  the  "grand'' 
j)iano.  causes  each  of  the  hammers  to  strike  on  one  less  string 
than  it  does  normallv.     Svmpathetic  vibrations  in   ^    ,., 

i  Quality 

the  string  thus  left  free  give  a  peculiarly  delicate  °^  ^°"^- 
flavor  to  the  tone;  otherwise  the  ])iano  tone  is  susceptible  of 
little  variation  in  quality.  Its  availabilitv  as  a  hcnisehold  in- 
strument, its  power  of  suggesting  harmonically  all  forms  of 
music,  its  usefulness  for  accompaniments  and  its  large  reper- 
torv  of  important  solo  compositions  account  for  the  wide  pop- 
ularity and  influence  of  the  ]iiano. 

All  the  in>truments  thus  far  studied  give  tones  of  an  cx- 
piosiir  character,  since  the  vibrations  of  the  strings  rapidly 
die  awav  after  their  first  impttlse  :  hence  the  performer  has  no 


126 


SOUND.  AND  ITS  RELATION  TO  MUSIC 


Means  of 

stopping 

vibrations. 


direct  power  of  sustaining  a  tone  and  can  only 
suggest  this  imitatively.  as  by  rapidly  repeating 
the  given  impulse.  Since  the  harp  and  pian(_> 
tones,  although  greatly  weakened.  }et  continue  for  some  time 
after  the  strings  have  been  excited,  means  for  stopping  the 
vibrations  must  be  provided  to  prevent  confusion  of  sounds. 
The  hari)ist  accomplishes  this  result  Ijy  laxing  the  ])alms  of 
his  hands  on  the  strings  immediately  after  thev  are  sounded; 
while,  in  the  piano,  dampers  connected  with  the  individual  ke}-s 
descend  upon  the  strings  when  the  keys  are  released,  except 
when  all  these  dampers  are  suspended  by  the  mechanism  of  the 
so-called  "loud  pedal."  Althotigh  the  office  of  this  ])edal  i< 
thtis  primarih-  to  allow  a  tone  to  continue,  its  use  also  results 
in  the  reinforcement  c^f  a  given  tone  by  the  partials  of  other 
strings  in  unison  with  it. 

Of  all  manufactured  instruments  those  j^ilayed  with   a  Ijow 
allow  the  performer  the  most  absolute  command  over  the  tone 
which  he  producer.      Hence  in  the  develo])ment 
of    the  orchestra    the 
'"strings."    as    they    are     po])ularly 
called,  soon  took  lirst  place,  resolv- 
ing themselves  into  the  four  forms 
which  are  em])lo\ed  at  ]M-escnt.  the 
liolin.  viola.  z'ioUmccUo  and  double 
bass. 

Considering    first    the    ^'iolin.    as 

the  most  imjxirtant  member  nt  thi< 

famih-    (  Fig.   *\3  )    we 

The    violin.  -       ,      ',  •        , 

tind  tliat  It  n;i^  t(un- 
strings,  the  three  tij^per  of  ])lain  gut 
and  the  lowest  wound  with  fmc 
wire. 

Tliev  arc  tuned  thus : 


Fig.    93.    violin. 
Lt'iicth  .  2 'i  in.:  ltn,trtli  of  how.  29i  in 


Bowed 
instruments 


SOUND,  AND  ITS  RELATION  TO  MUSIC  127 

Brilliant  and  ethereal  tones  are  produced  from  the  highest 
string,  the  others  diminishing  in  vividness,  and  the  lowest 
having  a  rich  and  sombre  (juality.  X'ibrations  are  induced  by 
the  rosined  horse-hairs  of  the  bow,  and  are  communicated 
through  the  bridge  to  the  resonating  body  of  the  instrument. 
The  air  within  this  also  serves  as  a  resonator,  as  may  be 
proved  by  blowing  across  one  of  the  two  vents  called  "F 
holes."  Many  violins  are  found  to  possess  special  resonance 
for  one  or  two  tones,  although  this  property  is  not  considered 
desirable. 

Diilerent  scale-tones  are  obtained,  as  on  the  guitar  and 
mandolin,  by  pressing  the  strings  upon  the  finger-board  with 
the  lingers  of  the  left  hand ;  but  in  the  case  of 

,.,.,,  .      .  Its  fingering. 

the  violm  the  absence  of  frets  at  once  makes 
greater  demands  upon  the  musical  sense  of  the  perfornrer  and 
at  the  same  time  opens  greater  possibilities  in  the  direction  of 
sliding  from  one  tone  to  another  or  slightly  varying  the  pitch 
of  a  tone.  The  latter  effect  is  used  in  the  vibrato,  made  by 
oscillating  the  finger  to  and  fro  on  the  string. 

The  normal  range  of  the  violin  is  about  Zy2  octaves,  extend- 
ing to  r".  This  range  may  be  pushed  somewhat  further  by  the 
use   of   harmonics,    wdiich    result    from   touching 

,  .  ....  ,        ^  .  .       Its  compass. 

the  strmg  at  nodel  pomts  mstead  of  pressmg  it 
down. 

Several  conditions  contribute  toward  the  quality  of  the 
violin  tone.  Purity  is  favored  by 'drawing  the  bow  straight 
across  the  string,  since  lengthwise  vibrations,  ^^^^g, 
otherwise  excited,  introduce  "scratchy''  elements,  possibilities. 
In  light  passages  the  bow  is  held  obliquely,  so  that  only  the 
hairs  on  one  edge  touch  the  strings,  while  in  forte  passages 
the  tone  is  increased  by  bringing  more  of  the  hairs  to  bear 
upon  them.  The  speed  and  pressure  of  the  bow  are  also 
determining  factors,  as  is  its  location  on  the  string.  Bowing 
near  the  bridge  produces  brilliant  overtones,  while  the  quality 
grows  softer  and  more  flute-like  as  the  finger-board  is  ap- 
proached.      Ordinarily    a    position    about    an    inch     from    the 


128  SOUND,  AND  ITS  RELATION  TO  MUSIC 

bridge  gives  the  best  results.  Roughness  of  the  bow  or  im- 
l^erfections  in  the  structure  of  the  vioHn  may  seriously  impair 
the  quality  of  tone.  Even  an  e.xpert  violinist  cannot  produce 
satisfactorv  results  from  a  poor  instrument.  On  the  other 
hand,  a  violin  made  skillfully  of  hne  materials,  such  as  well- 
seasoned  woods  and  enduring  varnish,  should  continually  im- 
prove with  proper  usage,  as  its  resonance  becomes  more  perfect. 
V>y  affixing  a  small  notched  clamp  of  metal,  called  a  mute. 
to  the  bridge,  the  vibrations  are  impeded  and  a  soft,  veiled 
quality  is  imparted  to  the  tone. 

It  is  important  that  the  constituents  of  all  the  violin-strings 
should  be  alike,  so  that  no  part  of  one  is  ditlerent  from  a  cor- 
responding part  of   another,   since   the  lingering 

Variations  in  111-  111 

structure  of  for  wholc  and  halt  steps  would  otlierwise  varv  on 

strings.  ,.  .  .  " 

ditterent  strmgs.  So  l"ng  as  all  the  strmgs  ahke 
become  thinner  where  the  bow  is  drawn  across  them,  for  in- 
stance, the  relative  distances  remain  constant,  but  if  a  string 
breaks  and  a  new  one  is  inserted  which  is  not  worn  as  are  the 
others,  difficultv  will  be  found  in  ])la}'ing  in  tune.  Hence 
skilled  performers  often  rei:»lacc  the  whole  set  of  strings  when 
one  of  them  breaks. 

Single  tones  are  made  possible  bv  the  rounded  form  of  the 
bridge.      Two  strings   side  b\-   side  may  be   sounded  together. 

but  when  three  or  four  tones  are  to  l)e  combined 

Special   effects.  ... 

arpeggiatmg  is  necessary.  A  tone  may  be  sus- 
tained for  anv  amount  of  time,  and  may  be  increased  or 
diminished  in  power  while  sounding.  Man}-  kinds  of  Icf/atc 
and  staccato  can  be  produced,  while  there  are  special  effects 
like  the  tremolo  or  >hivering  of  the  bow  on  the  strings  and  the 
saltaudo  or  jumping  bow.  In  the  l'i.z.::icato  the  violinist  plucks 
the  string-  with  his  fingers. 

Most   of    what   has   been    said    regarding   the   violin   ap])lic^ 
alsr)  to  the  other  orchestral  stringed  instruments.     Headed  b_\ 

the   i\r<t   and    seconrl   violin-,   the   tone   desceufl- 

Characteristics  .  1,111 

of  the  other  tlirougli  the  ^•lo!as,  violnncello.  and  double  Ijas-e- 

strings.  ^,       ,    '        .       ,  ,  ,      .  ,  . 

I'.acb    ot    the    la^t-name''    m-truments    has    lour 


SOUND,  AND  ITS  RELATION  TO  MUSIC 


129 


strings,  except  that  in  i'lngland  the  double  bass  frequently  has 
but  three.     The  tuning-  is  as  follows: 


Viola  ■Cell,,  Bass 

Notes  for  the  double  bass  are  written  an  octave  higher  than 
they  are  pla\ed.  hence  the  open  strings  sound  an  octa\e  lower 
than  is  indicated  above.  On  account  of  the  long  fmger  stretches 
the  double  bass  is  tuned  in  fourths  instead  of  fifths  as  are 
the  others.     Harmonics  are  used  somewhat  sparingly  on  the 


Fig.     94.      Violoncello 
Lengtli,   4   ft.  :   length   of   1  ow,   28   in. 


Fig.    95.      Douhle-Tlass. 
L,enKth,  6  ft.  5  in.;   knKth  of  fx)w,  2^h  iu 


130  SOUND,  AND  ITS  RELATION  TO  MUSIC 

viola  and  violoncello,  but  are  harsh  and  unmusical  on  the 
bass.  The  latter  retains  the  old  viol  form  of  a  flat  back  and 
sloping  shoulders,  while  all  the  other  strings  have  high  shoul- 
ders and  arched  front  and  back.  Mutes  are  employed  with  the 
viola  and  violoncello,  but  are  impracticable  for  the  bass,  on 
account  of  their  necessarilv  large  size. 

The  -z'tola  stands  toward  the  violin  in  the  relation  of  alto  to 

soprano.     Its  thicker  strings  give  a  fuller  and  more  penetrating 

tone  than  that  of  the  violin,  and  while  its  range 

The  viola. 

is  about  three  octaves,  extending  to  r'",  its  highest 
tones  are  seldom  heard.  Tt  is  not  ordinariU-  used  alone,  but 
(jccasionally  renders  individtial  passages  with  finely  expressive 
effect. 

On  the  other  hand,  the  zioloiiccllo  {I'ig.  94)  is  especially- 
distinguished  as  a  solo  instrument.     It  is  used  throughout  its 

orchestral    range,    which    extends    to    about    e" . 

The  violoncello.  .       ,   .      ,.^    .  ,  .  ,  ,  ,  ,      , 

although  this  limit  mav  be  considerabi}'  extended  ; 
and  in  the  orchestra  it  sometimes  soars  even  above  vit)]as  and 
violins.  The  strength  and  richness  of  its  tones  make  it  valu- 
able for  melodic  ex])ression,  while  under  the  fingers  of  a 
skilled  i)layer  it  may  render  rapid  [)assages  with  great  bril- 
liancy. 

To  the  double  bass  (big.  95)  is  ordinarily  given  the  task 
r)f  furnishing  the  foundational  tones  of  the  harmony.  Its 
„,     ,    .,  range  extends  to  about  /'?.     Sustained  tones  are 

The  double  * 

•^^^^^  varied   by   occasional   pi.z::icato    effects,      lleetho- 

\'en  introduced  the  fashion  of  gi\'ing  t(.)  the  bass  rushing  scale 
passages  which  stand  out  with  great  power.  Modern  com- 
posers have  secured  weird  and  characteristic  cft'ects  by  divid- 
ing ihe  basses  into  separate  groups. 

We  must  now  treat  of  a  numerous  class  of  instruments  in 

wliich   the   tones   are   produced   by   z'lbrating   coinnvis   cf   air. 

There  are  two  divi:;ions  of  these,  named  resiKH-t- 

Vibrating  ' 

air-columns.  ivcK'    the    '' wood-wiiid"    and    the    "bras-,""    from 

the  materials  of  which  thev  are  constructed. 


SOUND.  AND  ITS  RELATION  TO  MUSIC  131 

Three  groups  of  instruments  make  up  the  wood-wind,  of 
which  we  shall  first  study  the  fliitc  faniilv,  headed 

■^  "  The  wood-wind. 

1)\    the  modern  concert  flute. 

The  latter  consists  of  a  long  narrow  tube  having  the  same 
diameter  throughout  (Fig.  96).  One  end  is  closed,  while  the 
other  is  left  open ;  and  near  the  closed  end  is  a 

'  .  .        The  flute. 

circular  orifice  across  which  the  ])layer  blows,  m 
order  to  set  the   interior  air  into   vibration.      l>y  opening  or 
closing   six    smaller   holes,    of    which    the    player   manipulates 

three    with     the 

hand,  the  length 

Fig.    96.     Boehm  Flute.     Length,  26i  in.  ^£       ^y^Q      air-col- 

umn  is  changed  and  the  tones  of  the  diatonic  scale  are  formed. 
Other  holes,  closed  by  valves,  may  be  opened  to  obtain  chro- 
matic notes. 

Starting  at  c'  the  range  extends  upward  to  about  tib'^  Por 
the  lowest  octave  the  fundamental  tones  are  used ;  but  to  sound 
tones    in    the    second   octave    it    is    necessarv    to    ,. 

Its   registers 

"overblow"  the  instrument,  so  that  the  first  upper  ^"'^  quality, 
partials  are  heard  instead  of  the  fundamentals.  Still  higher 
partials  are  evoked  through  the  rest  of  the  compass.  While 
the  form  of  the  flute  would  naturally  give  rise  to  the  entire 
series  of  upper  partials,  the  friction  of  the  air  along  the  sides 
of  the  narrow  bore  destro}  s  most  of  them,  so  that  in  the  lower 
octave  or  "register"  the  tone  is  sonorous  but  somewhat  hollow, 
the  middle  register  is  sweet  and  melodious,  and  the  highest 
register  is  more  brilliant  and  1)ird-like. 

Formerly  made  of  wood,  flutes  are  now  constructed  also  of 
metal.  Most  agile  of  all  wind  instruments,  they  are  at  home  in 
all  kinds  of  running  ])assages  and  in  quicklv  re- 

1  (.1        1  1      '"  !••  -i^M   -1      '  1     Its  possibilities. 

peated  or     double-tongued     notes.      W  hue  used 
in  the  orchestra  to  give  brilliancy  by  reinforcing  the  tones  of 
other  instruments,  the  flute  also  renders  solo  melodies  or  runs 
with  much  charm. 

A  small  flute  called  the  piccolo  (Fig.  ""'"V  having  a  compass 


132 


SOUND.  AND  ITS  RELATION  TO  MUSIC 


The  piccolo. 


Fig.    97.     Piccolo.     L^iiKth    12Hii 


an  octave  higher  than  the  instrument  ju.st  de.scribed,  is  the 
only  other  member  of  this  family  which  has 
orchestral     significance.       Its    clear    and     sharp 

middle   register  is  useful   for 

special    effects,    such    as    the      E^^U-^l^g^^^i^ 

whistling  of  the  wind  or  the 

rustling  of  leaves. 

Next  among  the  wood-wind  comes  the  oboe  family.     This 

has  four  principal  members,  all  conical  in  form,  enlarging 
graduallv  from  the  mouth-piece  to  the  other  end. 

Characteristics         ^    ,.,.',,      ,  ,         ,,,,      .  ,.      .  .    ,   . 

of  the  oboe  which  IS  Ijeil-shaped.      i  heir  most  distinguishing 

characteristic,  however,  is  the  doul^le  reed  which 
acts  as  the  motor  and  which  consists  of  two  thin  sli])s 
of  cane  ])laced  nearly  in  contact  and  attached  by  silk 
to  a  small  brass  tube  that  is  inserted  in  the  end  oi  the 
wooden  part  of  the  instrument.  The  i)la}er,  hfjlding 
this  reed  in  his  mouth,  breathes  genll\-  into  it.  pro- 
ducing vibrations  which  cause  the  air  in  the  main  tuljc 
to  sound.  Regulated  in  length  by  holes  and  ke\s  ar- 
ranged on  the  same  ])rinciple  as  those  of  the  flute. 
the  air-column  gives  out  tones  of  different  ])itche.s. 
forcing  the  flexible  reed  to  conform  to  its  vibrations 
(page  78).  .V  penetrating  c|uality  results  from  the 
emphasis  of  high  upper  partials  in  the  full  harmonic 
series  that  is  ])resent. 

The  ohoc  proper  (Fig.  98)   is  the  treble  mcml)er  nf 

this   family,   having   a   normal   range    from   hh   U)   (/'". 

When  the  flnner  holes  are  opened  in  the 

The    oboe.  '    .  ,  -    tx 

])roper  succession   tlie  scale  ot    1)  major 
is  sounded.     r)ther  tones  are  produced  by   u.-^ing  the 
keys.     Three  registers  are  formerl  as  in  the  ca-c  of  tlie  ^-s-  ^^■ 
flute  and   of  these  the  middle  is  the  most  agreeable.   i,e:;-tii, 
since  tiie  lower  is  harsh  and  tlie  up])er  piercing.      Its    -■*-^  '" 
dominant  character  makes  the  <il)oe  largely  a  solo  instrument. 
in    which    capacit\-    it    is    especialK-    identified    with    exjjressive 
melodies    of    a    pastoral    style.      Moderatelv    (|uick    ■-cale    and 


SOUND,  AND  ITS  [RELATION  TO  MUSIC 


133 


arpeggio  passages  are  possible,  although  difficulties  are  exper- 
ienced in  connection  with  remote  fiat  keys.  Owing  to 
the  small  amount  of  air  necessary  to  excite  vibrations, 
the  player  is  obliged  constantly  to  hold  his  breath  in 
check,  and  must  therefore  frequently  cease  playing,  to 
avoid   undue  strain. 

Identical  with  the  oboe  in  shape,  except  that  it  is 
somewhat  larger  and  has  a  bent  crook  for  a  mouth- 
piece, is  the  English  horn  (Fig.  99).  Its  ^^^  ^^^^.^^ 
compass  is  a  fifth  lower  than  that  of  the  ^°''"- 
oboe,  to  wdiich  it  acts  as  alto,  and  extends  from  e  to 
h^".  For  convenience  in  changing  from  one  to  the 
other  instrument  its  notes  are  written  in  the  oboe  com- 
pass, so  that  each  actually  sovmds  a 
fifth  lower  than  it  is  notated.  Its 
tones,  less  brilliant  than  those  of  the 
oboe,  have  a  mystic,  melancholy 
character.  Quick  passages  are  un- 
suitable for  it. 
Fig.  99.        An   instrument  of  great  range  and 

Horn'(Cor  'is'i'i^y    '^    ^lic    bassooii,    the    bass    of 

AHKlais).  ^j^-^     ,-^^j^^ji^.     .p-  J  00). 

'r^pf  h  '        ,  .  .  The  bassoon. 

o;:  111.  {^g  tul)e,  nearly  nme  feet 
long,  is  given  a  more  available  shape  by 
doubling  it  upon  itself  so  that  it  resembles  a 
bundle  of  fagots  (whence  its  Italian  name  of 
fagotto).  A  brass  crook  connects  the  unusu- 
all\-  large  double  reed  with  the  wooden  tube. 
The  compass  of  three  octaves,  from  i?b,  to 
b'o\  has  the  usual  three  registers,  of  which 
the  lowest  is  thick  and  unmanageable  in  the 
lower  tones,  the  middle  melodious,  and  the  upper  sweet,  re- 
sembling in  quality  the  tones  of  the  violoncello.  There  is 
much  varietv   in  the  orchestral  use  of   the  bassoon.      It   mav 


Fig.    100. 

Bassoon. 

IvCngth,  4  ft.  4  in. 


134 


SOUND.  AND  ITS  RELATION  TO  MUSIC 


furnish  the  bass  for  harmonies  or  reinforce  melodies,  or  it 
may  play  solo  melodies  or  runnmg  passages  which,  especially 
when  staccato,  have  a  humorous  effect  that  has 
earned  for  the  bassoon  the  epithet  of  ""clown  of 
the  orchestra."" 

Only  occasional!}-  does  the  low-pitched  contra- 
bassoon  appear  in  the  orchestra  (Fig.  101  ).  Pro- 
_,,  ,  portionalh-    an    octave    lower    than 

The   contra-  ' 

bassoon.  ^|-,g  bassoon,  its  range  is  only  from 

C,  to  E'o.     Owing  to  the  great  length  of  its  tube. 

which  is  about  sixteen   feet,   rapid  passages  are 

not  practicable. 
There  are  two   families  of    instruments  which 
have   as   motor   a   single,    rather   than    a 
„.    ,        ,  double    reed — the    clarinets 

Single-reea 

instruments.  'dud  ihe  saxo plioiics.    I  lead- 

ing   the    first    of    these    is    the    clarinet 
proper,  like  the  oboe  in  that  it  consists 
of   a   wooden   tube    with   a 
mouthpiece      at      the      end 
{Vw.    102).      In   the   mouthpiece,   which 

"  '■  i-ig.     101. 

is  of  wood  or  ebonite,  is  a  broad  strip  of  Contra-iias-oon. 
cane  narrowed  to  a  fine  edge  at  the  U])per  ivenKth.^ft. 
part.  I'ressed  against  the  lower  li])  of  the  i)erformer 
and  excited  bv  his  breath,  this  sets  into  sympathetic 
vibration  the  air-column  in  tlie  long  tulje,  to  which 
the  mouthpiece  is  affixed.  This  tube,  dillering  fr()m 
ihat  of  the  oboe,  is  in  the  form  oi  a  cxiinder  rather  than 
a  cone,  having  a  small  bell-sha])ed  end.  Its  difterence 
in  sha])c  causes  it  U)  stand  to  the  oboe  in  the  relation 
of  a  closed  pipe  tcj  an  open  ( i)age  (A),  witli  the  result 
that  its  tone  is  an  octave  lower  in  pitch  in  ])roi)ortion 
to  its  length,  and  that  onlv  the  odd  series  of  partials  i- 
produced. 

On  account  of  the  latter  fact  the  ke\-  mechanism  is 
unu^uallv  complicated:   for  since  the  tliird  partials.  at 


The  clarinet. 


SOUND.  AND  ITS  RliLATlON  TO  MUSIC  135 

distances  of  twelfths  above  the  fundamentals,  j^^  ^ 
are  the  ones  hrst  produced  by  overblowing,  the  mechansim. 
series  of  fundamental  tones  must  be  extended  through  a 
twelfth  in  order  to  meet  these  and  complete  the  scale.  For 
instance,  the  lowest  note  c  overblown  gives  b',  a  twelfth  above. 
The  result  is  the  formation  of  a  fourth  register,  as  shown 
in  Fig.   103. 


Fig.    103. 

Of  these   registers  the   (jravc  and   the  acute  are  the   most 
important,   since   the   dtill   character   of   the    medium    and   the 
piercing  qualit\-  of  the  highest  impair  them   for   j^^  re-^isters 
mtisical   ])urposcs.      Rich   and   mellow   tones   are   ^""^  quality, 
found   in   the  (jrcK'c   or  "chalumeau"  register,  while  those   of 
the  acute  arc  clear  and  round. 

( )wing  to  difficulties  in  lingering  the  performer  can  play  in 
only  a  limited  number  of  scale-keys  on  a  single  instrument: 
hence  clarinets  of  different  i)itches  are  provided.    ^ 

i  i  Transposing 

These  are  transposiuij  instruments:  that  is.  their  clarinets, 
luusic  is  written  as  if  for  the  clarinet  built  on  tlie  ('  scale. 
Indeed,  on  account  of  their  better  (juality  the  clarinets  in  B\> 
and  A  are  used  more  often  than  the  one  in  C,  the  lirst  sound- 
ing B^  and  the  second  ./  when  the  written  ('  is  i)layed.  and 
the  other  tones  maintaining  the   same  relative   distances. 

liesides  ])ossessing  exceptional  beatit}-  of  tone-quality,  the 
clarinet  is  able  to  graduate  the  inlensitv  of  its  tone  more  than 
anv  other  wir.d  instrument,     because  of  its  wide   _,     .,_.,.  . 

Possibilities 

range  and  ])ossibilities  of  ])assage  work  it  is  used    of  the  clarinet. 
in  military  bands  in  ])lace  of  the  violin.     Again,  its  sustaining 
power  is  exhibited  in  rich  and  ])oetic  melodic  work. 

Passing  over  the  alto  clariiief  or  basset  horn,  not  often  now 
used  in  the  orchestra,  we  come  to  the   bass  clarinet,   shaped 


136 


SOUND,  AND  ITS  RELATION  TO  MUSIC 


The  basset 
horn  and  bass 
clarinet. 


Saxophones. 


like  the  ordinary  clar- 
inet but  with  a  crook 
to  the  mouthpiece  and 
the  lower  end  bent  so  that  the  bell 
points  upward  (Fig.  104).  Sev- 
eral of  these  instruments  are  in  use, 
of  pitches  corresponding  to  those 
of  the  clarinets,  lait  an  octave  be- 
low them.  Their  rich  and  telling 
tones  sometimes  assert  the  bass  of 
the  harnion}-  and  sometimes  appear 
in  singing  melodies. 

Saxophones  are  employed  chiefly 
in  military  bands.  While  they  have 
a  single  reed,  they 
ditler  from  clarinets 
in  that  their  tubes  are  conical.  On 
account  of  their  shape  the\-  are  gen- 
erallv  classed  among  the  wood- 
wind, although  they  are  made  of 
brass. 

Brass  instnoiiciits  ditter  from 
the  wood-wind  chiefl}-  in  the  man- 
ner   in    which    their   vibrations    are       ^^'' 

excited.     Each  consists  of  a  conical  tube  ending 

)\-  a  metal  mouthpiece. 
\'ibrations  are  excited  in  the  latter  l)y  the  li])s  of 
the  pla}'er,  and  are  thence  transmitted  to  the  air  in  the  tubing. 
Acting  as  membranous  reeds,  the  li])s  ])riMlucc  1)\'  their  ])roper 
adjustment  or  cuibrocluirc  the  \-arious  tcnos  of  the  harmonic 
series.  generalK-  ol)taining  the  fundamental  either  not  at  all  or 
\\'ith   difticult}'. 

When   the   mouthpiece   is    funnel-shaped   and   the   tube    \'er\- 
long  in  ])roportion  to  its  diameter,  the  production  of  tlie  higher 
partials    is    favcircd.      .^uch    condition-    exist    in 
the  "natural"  Jioni.  of  which  the  tubing,  coiled 


Fig.    104. 
clarinet.     Lentrth,  3  ft.  ?  in. 


Characteristics  .  ,      ,, 

of  brass  ui    a   bcll    and    ca])]K'd 

instruments. 


The     natural 
horn. 


SOU.WD,  AND  ITS  RELATION  TO  MUSIC 


137 


up  for  convenience,  is  from  9  to  12  feet  in  length.  With 
the  "natural"  horn,  employed  by  the  classic  masters,  it  is  im- 
possible without  altering  the  length  of  the  tube  to  play  the 
harmonics  in  more  than  one  key,  although  an}-  tone  may  be 
dropped  a  half  step  in  pitch  by  thrusting  the  hand  into  the 
bell  and  thus  producing  ■"stopped"  tones,  muffled  in  quality. 
Normally  tuned  in  C,  the  natural  horn  is  made  to  sound  in 
other  scales  when  its  tube  is  lengthened  bv  the  insertion  of 
metal  "crooks."  Like  the  clarinet  it  then  becomes  a  trans- 
posing instrument,  since  its  music  is  still  written  in  C.  although 
sounding  in  a  ditferent  key.  F'.ach  note  of  the  horn  in  F,  for 
instance,  sounds  a  fifth  lower  than  written.  The  horns  in 
F,  E  and  E^  are  the  most  common. 

In  the  modern  orchestra  the  I'ak'c  horn,  popularly  known 

as  the  FrcncJi  horn  (Fig.  105), 
is  generally  employed  in  place 
of  the  natural  horn.  ^^^  ^^^^^ 
It  was  first  em-  ^°''"- 
ployed  by  Halevy  in  La  Juivc, 
1835,  and*  Schumann  was  the 
first  German  composer  to  vise  it. 
Bv  the  use  of  three  pistons 
which,  when  pressed  down  singly 
or  in  combination,  change  the 
pitch  anywhere  from  one  to  s' 
semitones  the  trouble  of  insert- 
ing different  crooks  is  obvi:,ted. 
Thus  the  player  is  able  to  obtain 
the  full  chromatic  scale  without 
difficulty.  On  the  valve  horn  in 
F,  for  instance,  all  the  tones 
from  Bi  to  c"  derived  from  the 
fourth  to  the  twelfth  partials,  can  be  played,  while  the 
second  and  third  partials  are  also  possible.  Horns  are  used  in 
pairs  in  the  orchestra,  half  the  players  taking  the  higher  notes 
and    the    others    the    lower;    since    on    account    of    difficulties 


Fig.    105.      Valve-horn. 

I.en^rth,  22\  in. 


138 


SOUND,  AND  ITS  RELATION  TO  MUSIC 


The    trumpet. 


in  adjusting;  the  lips  players  j^refer  to  specialize  in  certain 
l)arts  of  the  scale.  I'he  mellow  yet  sonorous  tones  of  the  horn 
are  sometimes  used  in  lively  ])assages,  such  as  hunting  fan- 
fares, but  are  still  more  effective  in  solo  melodies  of  a  sus- 
tained character. 

A  kindred  brass  instrument  is  the  trumpet,  which  differs 
from  the  horn  in  that  its  tube  is  but  half  as  long  and  is  bent 
dift'erently.  The  diameter  of  the  tube  is  but  }i 
of  an  inch  from  the  mouth])iece  until  it  ap- 
])roaches  tlie  l)cll.  when  it  widens  out.  The  mouthpiece  is 
shai)ed  hemispherically,  like  a  cup.  I'.y  the  trumjjet  in  C  the 
full  series  of  upper 
])arti.als  as  far  as 
the  twelfth  is  ob- 
tainable, w  bile 
those  in  other  keys  ^.__.    ,.,    .,,  ,     . 

•^  b:o.     106.      Valve-tniiiipet. 

are    made    ])ossible  i.enjjth,  22!:  in. 

by  the  addition  of  crooks,  in  which  case  the  written  music 
is  transposed.  \'al\-e-trtmii)ets  (  I'ig.  106)  are  now  generally 
used  in  place  of  the  original  "naturar"  instruments,  with  the 
])reference  gi\'en  to  those  in  />''  and  .  /.  The  ])ractical  range 
is  from  c  to  about  b'^" . 

The  louder  tones  of  the  trumpet  have  a  ringing  (|uality  that 
easily   dominates  the   full   orchestra;   while  the   clearness   and 
ptu'itv  of  its  soft  tones  arc  em])loyed  for  distant 
or  mystical  effects. 

All  the  otlier  brass  instruments  have  cup-shaped  mouth- 
])ieces,  and  tubes  of  which  the  bore  is  of  greater  diameter 
„,        ,    .  ^.  than    that    of    the    horn    or    the    trumpet.      The 

Characteristic  ' 

of  the  other         effect   of   this   Condition    is   to   i)ro(luce   tones   of 

brass  instru-  ' 

™^""-  a    full    and    round    qualitx-   but    lacking   the    bril- 

liancy gi\-en  b\-  the  high  upper  partials. 

As  a  sub'^titute  for  the  trum])ct  the  cornet  is  frecjuently  used 

on  account  of  the  facilit\-  \vith  which  it  can  be  played,  exceeding 

that   of  an\-  other  bra-^s  instrument.      Of  the  B'f> 

The   cornet.  "  . 

cornet  the  tube  is  but  4'  j    feet  long,  so  that  its 


Its    quality. 


SOUND,  AMJ  ITS  RILLATIOK  TO  ML'SIC 


139 


pitch  is  an  octave  liii^lier  than  that  of  the  corres])ouding 
trumpet.  In  most  other  resjiccts  llie  two  instruments  are 
similarly  constructed;  l)Ut  as  onl\-  the  lower  partials  are  ol)tain- 
ahlc  on  the  cornet  its  tone  is  far  less  commanding;'  and  sensitive 
in  (luality. 

In  the  trombone  (  I'ig.  107)  very  perfect  intonation  is  made 
])ossil)le  1)\'  a  long'  sliding  section  of  tuhe  wl'iich  fits  closely 
into  the  original  tul)e  of  the   instrument,  and  is 

.       ,  .  Tlie    trombone. 

])erlectl\-    under    the    control    ol    the    jjertormer. 

When  this  slide  is  closed  the  instrument  is  said  to  he  in  the 

first  position,  in  which  case  the  fundamental  and  seven  ])artials 


Fig.    107.    Trombone. 
I.cTiKth,  clcsed,  3  ft.  9  in. 

can  be  obtained.  I'.y  pulling  out  the  slide,  six  other  positions 
are  produced,  each  sounding  tones  a  half  step  lower  than  the 
previous  one,  although  the  fundamental  is  not  obtainable  in 
the  lower  positions,  b'videntlv  the  same  tone  can  frequently 
be  produced  in  difi'erent  registers.  The  notes  are  sounded  as 
w  ritten. 

Of  several  sizes  in  which  trombones  are  made  the  tenor 
trombone  in  B'^  is  now  most  common,  sometimes  supplemented 
l)y  the  bass  trombone.  1'he  normal  compass  of 
the  former  is  from  /:  to  d"  and  of  the  latter 
from  B    to  /'.     Idie  trombone  tone  is  rich,  even  and  sonorous. 

Three  trombones  freciucntlv  form  a  c|uartcl  with  the  bass 
tuba  (I'^ig.  108),  to  produce  a  soul-stirring  combination  that 
resounds  above  the  entire  orchestra.     The  latterBBBBi^lBBi 

,      .  ,  ^  .  .     .  The   bass   tuba 

mammoth  instrument  has  four  pistons,  giving  a   and   the 

,  .  ,,  7  L/       T     1  ^  ophicleide. 

chromatic  range  from  /•    to  bo  .     It  has  now  sup-| 


Kinds    in    use. 


140 


SOUXD,  .IXD  ITS  KELATIOX  TO  MUSIC 


planted  the  savage  Ophidcide,  which  was  hngerecl  Ijv  holes 
in   the   sides. 

We  ha\e  now  to  si)eak  of 
those  wind  instruments  which 
T-,     .  are     ijlaved     bv     a 

I  he    narmon-  i        - 

ium,  American     kev-board  nicchan- 

organ    and 

concertina.  j^,-,-,_         J^^^^     impor- 

tant types  are  the  harmGnium, 
.Imcrican  rccd  onjau  anrl  con- 
ccrti)ia.  All  of  these  have  as 
vibrators  free  reeds  (page  77). 
which  are  somewhat  strident  in 
tone,  since  this  is  not  reinforced 
by  pi[)es.  In  the  harmonium  the 
air  is  forced  from  the  bellows 
through  the  reeds,  and  in  the 
American  organ  it  is  sucked 
through  the  reeds  into  the  bel- 
lows. Concertinas  are  furnished 
with  fourteen  notes  to  the  oc- 
tave, having  separate  reeds  for  Dt  and  7:5.  and  for  (/:;  and  Ai. 
The  most  elaburate  of  all  wind  instrumcnt>.  anrl  one  caj^able 
of  prrulucing  an  infinite  ^■arietv  of  ettects  throughout  its  entire 
„,       .  compass,   is   the   pit'C   orqaii.      Its   ti»ne>   are   ob- 

The    pipe  '  '     '  ■' 

•^■■s^"-  taincd    from   a  multitude  of   both   flue   and   reed 

pif)es,  the  latter  having  either  free  or  beating  reeds  i  page  77  i, 
and  all  \aricrl  in  qualit\-  by  (Htl"erence<  in  s]ia])c  and  materials. 
.A  row  oi  ])i])es  of  an\-  gi\'cn  r]ualitv  i-^  made  read}-  ii>r  action 
b\-  drawing  out  the  pr('])er  "sto]/" :  and  when  a  key  i<  de- 
pressed a  valve  is  opened  in  the  corre-^ponrling  pi]:)e.  thus 
allowing  the  wind  to  enter  which  cau-cs  the  i)!pe  to  "speak."" 
Stops  are  also  of  ditterent  ])itcbe-.  Tho^e  called  cii/ht-fnnt 
stops,  from  the  tlicoretical  length,  of  their  lowest  ])i])e,  gix'C  the 
pianoforte  pilch,  while  those  of  ,-ixteen  feet  give  an  octave 
lower,  those  of  four  feet  an  octaxc  higher,  and  -o  on.  Thus 
the  range  e.xtends  to  the  limits  of  auflibilit\-  in  either  direction, 


Fig.    108.     Bas>  Tuba 
I^enyth,  3  ft.  .^  in. 


SO('XI).  .INI)  ITS  RliL.rnOX'   TO  Mr  SIC 


141 


although  ihc  kc\hoards  or  manuals  each  cover  only  hve  (jc- 
taves.  These  manuals  vary  in  nuniher  froiu  one  to  tour,  and 
are  supplemented  h}'  a  row  ui  pedal  keys  2|j  octaves  in 
extent,  ])laye(l  hy  the  feet,  luich  manual  is  a  complete  organ 
in  itself,  although  comhinations  of  the  manuals  among  them- 
selves and  with  the  pedals  are  made  jjossihle.  Thtis  the  organ 
is  not  properlv  one  instrument  hut  a  group  of  instruments, 
placed  within  the  power  of  a  single  performer  1)\-  intricate 
mechanisms  that  govern  wind  sup])ly,  stop  and  ke_\'  action  and 
combinational  devices.  \W  the  develo])ment  of  its  limitless 
resoiu'ces  and  the  linal  ai)plication  of  electricity  to  sectire  its 
connections  the  organ  has  become  a  monument  to  the  mechani- 
cal  genius   of   man. 

h'inally  in  c)ur  catalogue  come  the  percussion  instniinents, 
which,  although  generally  productive  of  mere  sound  rather 
than   tone,   are  vet  often  necessarv   for  the  em-    Percussion 

,         .  .      ,         ,      ■  ,  ,  .'  -  ,.  instruments: 

])nasis  ot  rliythm  and  for  the  cappmg  ot  a  chmax.    drums. 

The  most  musical  of  these  are 
the  kcftle-dntms  or  timpani,  of 
which  at  least  two  are  fotmd 
in  the  orchestra  (Fig.  109). 
l'",ach  consists  of  a  large  and 
hollow  brass  ]iemis])herc  across 
which  is  stretched  a  membrane 
that  can  be  tuned  through  the 
compass  of  a  fifth  Ijy  keys  at 
the  sides.  b^elt  hammers  in]- 
pinging  upon  this  membrane 
produce  a  well-defined  tone, 
which  can  thus  em])hasize  im- 
l)ortant  points  in  tlic  comp.osi- 
tion>.     The  hass  dritni  and  snare 

drum    are    onl_\-    occasionally    employed    in    the    orchestra,    and 

have  no  definite  tone. 

Metallic   instruments   of   percussion   are   represented   in   tlie 

orchestra  by  \ariou<  kinds  of  bells,  the  triam/le.  cymbals,  and 


Fig.    109.      Kettle-drum. 
Diameter  of   head,  2il  ill.  and  27 


142 


SOUND.  AND  ITS  RhL.iriON  TO  MUSIC 


Metallic  U^^fif/^-     Many  sensational  devices  are  employed 

instruments.  1,^    niotlem    comjjosers     tor    special    illustrative 

eliects.    These,  however,  can  scarcely  be  classed  among-  musical 
instruments. 

The  following  table  shows  the  compass  of  the  princi-pal 
instruments  of  the  sym])honv  orchestra  of  to-day.  it  gives 
the  actual  ])itch  of  the  instruments  with  the  usual  range  for 
orchestral  purposes.     In  solo  work  the  range  is  more  extended. 


COMl'ASS  OF  THF.  INSTRUMKXT.S  OF  TIIP:  OKCHKSTRA 
(Showiiii;  ihe  actual  pitch  and  the  ranj,'i-  for  orchcstralpurpost-s) 


Strings 


Fig.  no. 


In  the  development  of  the  modern  orchestra  there  has  l)cen 
a  constant  advance  in  the  knowledge  of  how  to  combine 
instruments  most  elTectivel}-.  of  the  best  i)r()portions  in  which 
to  emi)l()y  them,  and  of  the  UK^st  etlective  means  of  utilizing 
thcii-  indix'idual  cliaracteristics.  Thus  the  orchestra  has  be- 
come   a    mammoth     instrument    which    is    ca])ablc    of    giving 


SOUND.  AND  ITS  RELATION  TO  MUSIC  143 

expression  to  every  shade  of  musical  feeling,  and  which, 
moreover,  when  combined  with  voices  by  a  genius  like  Wagner, 
apparently  attains  the  acme  of  intensity  in  the  utterance  of 
emotion. 


144  SOUXD,  AXD  ITS  RELATIOX  TO  MUSIC 

SUMMARY 

Let  us  close  with  a  restatement  <jf  the  groups  of  instruments 
just  studied.  Those  used  infre(iuentl\-  or  not  at  all  in  the 
orchestra  are  preceded  hy  an  asterisk  (  *  ).  After  each  orches- 
tral instrument  is  placed  a  number  indicating'  how  manv  of  its 
kind  are  listed  in  the  personnel  of  the  l>oston  Symphony 
(Jrchestra  (  1911  ).  With  the  conductor,  the  band  of  perform- 
ers in  this  organizati(jn  at  present  numbers  exactly  one  hundred. 

I.     Stringed  ixstiuments  ; 
Plucked : 
*Guitar. 
^Mandolin, 
Harp    (I). 
Struck: 

^Pianoforte. 
Bozi'cd  : 

\'ioIin    ( U)  first,   14  second), 
\'iola    (10). 
Violoncello   (10), 
Double   Bass    (8). 

II.     Wind  ixstki-MEXts: 
U'ood-i^iiid  : 

I-'lute   (4). 

Piccolo, 

Oboe   (3). 

English  Horn   (1), 

Bassoon   (3), 

Contra- Bassoon    (2)^ 

Clarinet    (3), 

Bass-Clarinet   (1), 
*Sa\<iphone. 
Brass  : 

Horn    (8), 

Trumpet    (4), 
*Cornct. 

Trombone   (3), 

Tuba    (n, 
*<"  )ph;cleide. 
Keyhoti)  d : 

*l  larmunium, 


SOUND.  AND  ITS  RELATION  TO  MUSIC  145 

*American  Reed  Organ, 

*Concertiiia, 

*Pipe  Organ. 

III.     Percussion   ixstklments  : 
Kettle-drums   (2), 
*I!ass   Drum. 
*Snare  Drum  (4), 
Metallic    Instruments. 

REFERENCE  LIST. 

Barton,  Chapter  8. 
La7'igiiac,  Chapter  2. 
Pole.  Chapter  4. 
Stone.  Chapter  1. 
Zahin,  scattered  references. 

For  detailed  accounts  of  instruments  and  their  use,  consult 
also  the  following- : 

Ch.-M.    Jl'idor,  "The   Technique  of   the   Modern   Orchestra." 

(Joseph  Williams,  London,  1906.) 
/:.  Front,  "The  Orchestra,"  2  volumes. 

(Augener  &  Co.,  London,   1897.) 
A'.  Schlesinger,  "The  Instruments  of  the  Modern  Orchestra."  vol.  1. 

(William    Reeves,   London,    1910.) 
D.  C  Mason.  "The  Orchestral   Instruments  and  What  They  Do." 

(The    I'.aker   and   Taylor   (  o..    Xew    \'ork,    1909.) 
II  .  J.  I fendi'i  so)i.  "The  Orchestra  and  Orchestral   Music." 

(Charles  Scribner's  Sons,  Xew  York,  1902.) 


INDEX 


Air,  velocity  of  sound  in,  12-16 
affected  !)y  slight  sounds,   17 
Air-Columns,    sounding,    2,    63-68, 

71-79 
in   instruments,   130-140 
Air-cnrrcnts,    reflection    from,    20, 

21 
Air-particles,  ()-10,    12,  39 
/Vnii^litudc  of  \ibrations,  Zl ,  38,  48 
.Arabian    scales.   91 
Articulation,   organs  of,   113,   116- 

118 
Audible    sounds,    limits   of,   28,  29, 

32 
Auditory   canal,    108,    113 
Auditory    nerve,   6,    113 
Auditory  ossicles,   109,   113 

Bach.   104 
Banjo,  82 

Bass  clarinet,   135,   136 
I'ass  drum,   141 
Basset  horn,  135 
Bassoon,   133,   134 
Beats,  44-49,  63.  98-101 
Bell.  Graham,  86 
Bells,  47,  52,  62,  63.  141 
Hoys,  Professor,  10 

Cagniard-Latonr.  25,  26 

Canals  semicircular    (of  ear),  111, 

113 
Chinese  scales.  90 
Chladni,  17.  43.  60,  61 
Chords,   101,   102 
Chromatic  notes,  2>2,  97 
Circle  of  fifths.  92 
Clarinet,  75,  134-136 
Clouds,  echoing,  20 
Cochlea,   lll-li3 
Comma   in   music,   92,  97,    103 
Concertina.    140 
Condensation,     waves     of.    7,     19, 

41-44.  52,  57,  64,  65,  71,  72 
Consonance,  98-102 
Consonants,   117,   118 
Contra-bassoon.  32,   134 
Cornet,   138,   139 


Cymbals.   141 
Darwin,   17 
Density,    12 

and   velocity,    14-17 

in    reflection,    19 

and  intensity,  39 
Diatonic  scales,  91,  95-97 
Diffraction.   22 
Discords,   45 
Dissonance.  98-103 
Double  bass,   126,   128-130 
Drum  cavity    (of   ear).    109 
Drumskin    (of   ear),  82,   109,   110, 
113 

Ear,  6,  48,  82.  108-113 

Ear   trumpet,   21 

Earth,  as   sound   transmitter,   17 

friction   of    wind    on,   40 
Echo,  14,  19,  20,  39 
Edison.   ^2 
Eidojihone.  118 
Elasticity.   3,    12 
English  horn,   133 
Epiglottis,   114.   115 
Equal  temperament,   103-105 
Eustachian  tubes,   109,   113.   115 
Explosions,  sound   from,    10 

of  meteors,  17 

sound-diffraction    from,   22 

Faraday.  79 

Flames,   sound    from,   78-80 

Flute,  51,  75,  131,  132 

Focus   of   sound,   18,    19,   22 

Fog-signals,   21 

F)-ench  Diapason  Xormal,  30,  31 

Galileo.  25 

Gas-flame,   reflection    from.    18.   20 

Gases,  sound  from.  2,  63,  64.  78-80 
as    sound-medium.    6 
velocity  in.   15.   16 
refraction   through,   21,  22 

Glottis,   114,   115.  117 

Gongs.   142 

Gramophone.   84.  85 

Graphic   vibrations,  27,  28 


148 


INDEX 


Greek   modes.   91-94 
(jrei^orian    modes,   93-95 
Guitar,    10,    124,    125 

Halcvy.   137 

Halls,  acoustics  of.  20 

Handel.  30 

Harmonics.    51,    52,    124,    125,    127, 

129,   137 
Harmonic  series.  56,  65,  67,  136 
Harmonium.    140 
Harp,  34,  124-126 
Head,     cavities    of    the,    86,     114, 

116 
Heat,  retiection  of,   17 

currents,   20.   39 
Hchul-oltz.    1.    27.    2i^.   48,    51,    53, 

75,  76.  97-99.  101.  104 
Ilciiioiiy.   63 
Hexachordal   scales.   95 
Hindoo  scales.  91 
Horn,    "natural."    136.    137 

\alve  or  French.   137.   138 
Hughes.  Mrs.    Watts,   118 

Incidence,   law   of.    17,    18 
Inharmonic  partials.  52.  54.  59,  63 
Insects,    sound    produced   by,    17 
Instruments,  4.  5,  33-35.  45,  47.  51, 
123 
stringed.  23.  82.    123-130 
wind.  63.  64.  75-78.   130-141 
keyboard,   54.    102-104,    125,    140, 

"Ml 
I)crcussion.   5.   63.    141.    142 
Intensity,    see    loudness 
Interference,   40-48.  98 
International    pitch.   30.   31.   56 
Interxals   in  music,  89-106 
Impulses,    law    of    cumulative,   69- 
71 

Jaf)anese   scales,   91 

Ju^t    intonatir)n.   96.    102-105 

Kiistncr.  79 

Kettle-flrums,    141 

Kevborird     instrument^,     54,     102- 

"  104.   125.   140,   141 
Kocuui.   Dr..   ],   28.   46,   48,    52-54. 
74,   100 

r.ab\-rinth    i'"f   ear),    110 
l.arvnx,    114 


Light,  and  sound,   12,   13 

retiection  of,   17 
Lissajous,  46,   100 
Liquids,   sound  in,   16 
Lobe   (of  ear  >.  108 
Loudness   of   sound,   in   reflection, 
19 

degrees  of.  24 

at   night,   21.   39 

and   wind.   39 

laws   of.  37-39 

and   qualitv.    51-54 

of  voice.  86.   115.   116 

of  instruments.    123-142 

in  ear,   112 
Lungs.   113.   116 

Mandolin,    124,    125 
Mariottc,  8 
Marloyc.  61 

McKendrick.   Prof..   85 
Mean-tone   temperament,   103,   104 
Membranes,   21.   43,   63,   67,   82-86, 
lis.   141 

in   ear.    109-112 

in   head.    116 
I\Iersen)ie.    14 
Melndiaphone,  75 
Melodic   progressions,   89 
Metallophone,  60 
Metals    as   soimd-confluctors.    16 
Miraf/e.  /};-,.    118 

Mirrors  as  sound-reilectors,  18,  19 
Modes,   see  scales 
Modulation.   97.    102-104 
Moisture,   its   effect   on   soinid,    13, 

21 
Monochord.   33.  92 
Mouth,   86.    114,    117 
Mocart.   30 

Musical  and  non-musical  sounds,  4 
Music-box.    16.   81 

Xasal   ca\-ities,    114-116 
Xeietou.  .Sir  I  sane.  14 
Nodes,  55-68,  75.  124,  127 
Xoi^e  distingiu'shed  from  tone,  4.  5 
Notation,  names  of  octaves,  29,30 

O],oe,  51.  75.  132-134 
Dphiclcide,    140 
Orchestra,    51,    105.    142-145 
Or.fran,    see    pipe    organ    and    reed 
organ 


IXDEX 


149 


Organ  pipes,  43,  44,  67,  74,  78,  140 
Origin  of  sound,  1-5 
Oscillations,   of   bar,  6 

of   water-particles,  8 

of  pendulums,  69,  70 
Overtones,  see  partials 

Palate,   hard   and   soft,    114-117 
Partials,   47,    51-().S,    77,   79-81,   85, 
95,  96,  99 

of   instruments,   124-139 
Pendulums,   experiments   with,   70, 

80 
Pentatonic   scale,  90,  91 
Percussion  instrume".ts,  5,  63,  141, 

142 
Pharyn.x,   114,  115 
Phase,  of  sound-waves,  52,  62 
Phonautograph,  83 
Phonograph,  82-86 
Phvsical  basis  of   sound,   1 
Pianoforte,  29,   30,  32.  34.  45,  58, 

74.  81,  82,  99,   123,   125,   126 
Piccolo,  32,   131,   132 
Pipe  organ,  30.  44,  10^3,  140,  141 

of   singing  flames,  79 
Pitch,  14,  20,  24-36,  41,  47.  51,  53, 
56.  60,  62,  67.  71,  77.  78,  80 

in  the  ear,  112 

of  scale-tones,  89-106 

of  voice,  115,  117,  118,  120 

of   instruments,   123-142 
Plates,  metal.  43,  52,  61-63 
Power   of   sound   affected   by   res- 
onance,  20 
Pulsation  atid  music,  5 
Pythagoras,   1,  33,  91,  92.  96,   103 

Quality,  20,  24,   51-68,  77 
in  phonograph,  85 
in  ear,   112 
of  voice,  86.   115-121 
of    instruments.    123-142 

Rarefaction,  waves  of,  7,  19.  41- 
44,  52.  57.  (4.  65,  71.  72 

Raritv  of  air  and  sound-intensitv. 
39 

Receiver,   of   telenhotie.   86 

Reeds,  76-78,  115,   132-136,  140 

Reed  organ,  47.  140 

Reflection    of    sound.    17-21.    41 

Refraction  of   sound,   21,   22 


Regiiaiilt,  39 

Resonance,  20^  40,  69-88 
in  voice,  115-12i 
in   instruments,    123-143 

Resonators,    52-54.    72-75,    81,    98 
113-120,  123,  125,  127 

Resultant  tones,  47,  48,  99,  102 

Rhythm,   5 

Rods,  sounding,  6,  7,  35,  52,  58-61, 
65 

Sand  figures,  62 
S  a  live  It  r.  Joseph,  51 
Sa-cvrt.  25,  60,  72 
Saxophones,   134,   136 
Scale.-,,  30.  47.  89-97,  102-107 
Scheibler.   28 

Scheibler  Stuttgart  pitch,  31,  32 
Schionanii,  137 
Scientific  pitch,  32,  56 
Scotland,  pentatonic  scale  in,  91 
Seasliell.  singing  of.   75 
Sensations  of  tone.  The.  1 
Silence  zone,  20 

Shi.gers,  30,  97.  105,  117.  118.  120 
Sinuses    (of   head).   114.    116 
Siren.  5,  25-27.  97-99 
Snare  drum.   141 
Solids,   as   sound-transmitters,  6 
velocity  of   soinid   in,   16 
echoes    from,   20 
Sondhaus.  21 

Sonometer.  33.  54.  55.  74.  92 
Sounding   boards.  82,   125 
Sound-mill.  74.  75 
Sound-shadows.    22 
Speaking  trumpets.  21 
Speaking  tubes.  39 
Standards  of   pitch.  30-32 
Steatite  burner.   80 
Stringed   instruments.   33.  82.   123- 

130 
Strings,  stretched.  1.   16.  33-35.  45. 

54-58.  81.  82.  92 
String  telephone.  16 
Susceptibilitv     of     individuals     to 

pitch.   29 
Sympathetic   vibration,   see   reson- 

0)1  ce 


Tarfiiii's      tones. 

tones 
Telephone.  82,  86 
string.   16 


see      resultant 


150 


INDEX 


Temperature,   its  effect  on   sound- 
velocity,   13 
l)ro(luctive   of   reflection,  20 
Tempered   scales,  96,   103-105 
Tension  of  strings,   law  of,  34 
Tcrpaiidcr,  91 

Thickness  of  strings,  law  of,  34 
Throat,   80,    114 
Thunder  storms,   14,  20 
Tonality,  95,  97,  102,  104 
Tones,   nature  of,  4 
production   of,   7 
deafness   toward,  29 
relations  of,  33 
summational,      differential      and 

beat    tones,    48 
(jualitv  of,  51-53 
Tongue,   114,   116,   117 

-bone.   11() 
Tonometer,  28,  45 
Transmitter    (of   telephone),  86 
Transmission    ol    sound,    5-11,   63. 

74,  108,  110,   136 
Transi)()sing  instruments,  135,  137, 

138 
Triads,    101.   102 
Triangle,   141 
Troml)()nes.    139 
Trumpets,  51,   138.   139 
speaking  and   ear,   21 
Tuba,  bass.  139.  140 
Tubes,    sonorous,    21,    35.    39     60, 

61,  64-67.  72.  75.  77-79.  134 
Tuning-forks.    2,    3,    7,    27-29.    37, 
41-43.    45,    46.    53,    54,    59-60, 
70-74.  81,  100 
Tyuciall.   1,   20,  79 

/  'an  dcr  iiJicyn,  ()3 
\'elocity   of   sound,    12-17,  64.   72 
Ventral    segments.    55-66 
Vestibule   (of  ear),   110.   111.   113 
Vibrations    r)f    sound,    nature    of, 
2-6.  8 

fra\cling  ])ower,   17 

frecincncv,    24-28 

limits    of    audible.    28-29 

standard    rate.   30-32 

of  strings.  33-35.  54-58 

of   rods,  35.   58-61 

of   plates,  bells   and  membranes. 
61-63 


of  tubes,  35,  64-67 

of  reeds,  77,  78 

loudness   and,   37 

interference  of,  40-48 

relations  of,  51,  52 

in     phonograph     and     telephone, 

82-86 
in  ear,   108,   110-113 
of  vocal  cords,   115 
of  violin,   127 
means   for  stopping,   126 

Viola,    126,    128-130 

Violin.  4,  1(),  24,  25,  34,  37.  51,  57. 

82,  105,  126-128,  130,  135 
Violoncello,    12().    128-130.    133 
Vocal  cords,  113-115,   119 
Voice.  4.  7\<.  8(.,  108.  113-123 
Vowel   sounds,  i3,  o4,   117,   118 

Way  Iter.    143 

Water.    velocit\'    of    sound    in,    15, 

16 
Waves  of  sound,  7.  8,   10 
velocity  of,    12-17 
alTected    in    \arious   ways.    17-22, 

31.   33.   38-40 
interference  of.  40-48 
in   resonators.   53 
from   vibrating  strings,  57 
in   tubes,  64-()7.   71.   71 
from  tuning- l"i irks.  70-74 
from   reeds.    77 
in    ear.    112,    113 
Waves  of   water,  8,   19.  40 
Whcch-r.   liih.'urd   S..  86 
Whispering    galleries.    19 
Whistle.       for      measm-ing      acute 
sotuuls,  29 
of    engine,    33 
A\  iiul,    its    effect    on    soimd-veloc- 
iiy.    13 
on   pitch.   31 
Wind-chest,    43.    44.    76 
Wind    instruments,    ()3     64,    7S-7?', 

130-141 
Windows    (of   ear).    109.    111.    113 
Windpipe.    114 

Woofl.    as    sound-conductor.    16 
as  resonator.  81,  82 

X\-lophone,  60 


FEB  141957 


